For gas turbines, the demand for high-performance, more efficient and longer-life turbine blades is increasing. This is especially so, now that there is a need for high-power and low-weight aircraft gas turbines. Thus, the search for improved design methodologies for the optimisation of combustor exit temperature profiles enjoys high priority. Traditional experimental methods are found to be too time-consuming and costly, and they do not always achieve near-optimal designs. In addition to the above deficiencies, methods based on semi-empirical correlations are found to be lacking in performing three-dimensional analyses and these methods cannot be used for parametric design optimisation. Computational fluid dynamics has established itself as a viable alternative to reduce the amount of experimentation needed, resulting in a reduction in the time scales and costs of the design process. Furthermore, computational fluid dynamics provides more insight into the flow process, which is not available through experimentation only. However, the fact remains that, because of the trial-and-error nature of adjusting the parameters of the traditional optimisation techniques used in this field, the designs reached cannot be called “optimum”. The trial-and-error process depends a great deal on the skill and experience of the designer. Also, the above technologies inhibit the improvement of the gas turbine power output by limiting the highest exit temperature possible, putting more pressure on turbine blade cooling technologies. This limitation to technology can be overcome by implementing a search algorithm capable of finding optimal design parameters. Such an algorithm will perform an optimum search prior to computational fluid dynamics analysis and rig testing. In this thesis, an efficient methodology is proposed for the design optimisation of a gas turbine combustor exit temperature profile. The methodology involves the combination of computational fluid dynamics with a gradient-based mathematical optimiser, using successive objective and constraint function approximations (Dynamic-Q) to obtain the optimum design. The methodology is tested on three cases, namely: (a) The first case involves the optimisation of the combustor exit temperature profile with two design variables related to the dilution holes, which is a common procedure. The combustor exit temperature profile was optimised, and the pattern factor improved, but pressure drop was very high. (b) The second case involves the optimisation of the combustor exit temperature profile with four design variables, one equality constraint and one inequality constraint based on pressure loss. The combustor exit temperature profile was also optimised within the constraints of pressure. Both the combustor exit temperature profile and pattern factor were improved. (c) The third case involves the optimisation of the combustor exit temperature profile with five design variables. The swirler angle and primary hole parameters were included in order to allow for the effect of the central toroidal recirculation zone on the combustor exit temperature profile. Pressure loss was also constrained to a certain maximum. The three cases show that a relatively recent mathematical optimiser (Dynamic-Q), combined with computational fluid dynamics, can be considered a strong alternative to the design optimisation of a gas turbine combustor exit temperature profile. This is due to the fact that the proposed methodology provides designs that can be called near-optimal, when compared with that yielded by traditional methods and computational fluid dynamics alone.