This paper describes a new control scheme for approximately optimal control (AOC) of nonlinear systems, convex control design (ConvCD). The key idea of ConvCD is to transform the approximate optimal control problem into a convex semi-definite programming (SDP) problem. Contrary to the majority of existing AOC designs where the problem that is addressed is to provide a control design which approximates the performance of the optimal controller by increasing the "controller complexity," the proposed approach addresses a different problem: given a controller of "fixed complexity" it provides a control design that renders the controller as close to the optimal as possible and, moreover, the resulted closed-loop system stable. Two numerical examples are used to show the effectiveness of the method.