PURPOSE : An area of great interest in current computational fluid dynamics research is that of free-surface modelling (FSM). Semi-implicit pressure-based FSM flow solvers typically involve the solution of a pressure correction equation. The latter being computationally intensive, the purpose of this paper is to involve the implementation and enhancement of an algebraic multigrid (AMG) method for its solution. DESIGN / METHODOLOGY / APPROACH : All AMG components were implemented via object-oriented C++ in a manner which ensures linear computational scalability and matrix-free storage. The developed technology was evaluated in two- and three-dimensions via application to a dam-break test case. FINDINGS : AMG performance was assessed via comparison of CPU cost to that of several other competitive sparse solvers. The standard AMG implementation proved inferior to other methods in three-dimensions, while the developed Freeze version achieved significant speed-ups and proved to be superior throughout. ORIGINALITY / VALUE : A so-called Freeze method was developed to address the computational overhead resulting from the dynamically changing coefficient matrix. The latter involves periodic AMG setup steps in a manner that results in a robust and efficient black-box solver.