This paper describes an algorithm for a general minimum fuel control problem. The objective function of the problem is represented by the functional: F-0(x, u) - F-0,F-1(x, u) + F-0,F-2(x, u) where F-0,F-1 is continuously differentiable with respect to states x and controls u, while F-0,F-2 includes the term integral(0)(1f) Sigma(i=1)(m) g(i)(t,x(t))\u(i)(t) -u(i)(r)(t)\dt. A direction of descent of the algorithm is found by solving a convex (possibly non-differentiable) optimization problem. An efficient version of a proximity algorithm is used to solve this sub-problem. State and terminal constraints are treated via a feasible directions approach and an exact penalty function respectively. The algorithm is globally convergent under minimal assumptions imposed on the problem. Every accumulation point of a sequence generated by the algorithm satisfies the combined strong-weak version of the maximum principle condition.