In this paper, a framework of convex optimization algorithm with a fixed time convergence rate is investigated. Given a strongly convex optimization problem, two control algorithms are developed to solve the problem within a fixed time of which the upper bound is theoretically obtained. Moreover, the fixed time convergence rate based algorithms are extended into the distributed manner which is applied to two typical distributed optimization problems including the resource allocation problem and the coordination optimization problem. Laplacian graph matrix is employed to the weighted gradient based and the coordination based distributed optimization algorithms. By developing the characteristic of the objective function, the upper bound of the fixed time convergence is derived. Two numerical examples are given to verify the main results.