This paper is concerned with the proximal-based approach to linear and finite-difference approximations of constrained convex optimal control problems. We consider control systems governed by ordinary differential equations in the presence of additional terminal/state inequalities and propose a numerical method derived from the proximal point algorithm. The aim of the paper is to study the convergence properties of the obtained conceptual algorithm and to show that it can be used to compute approximate optimal controls. © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society.