Abstarct: In this thesis, we solve a class of optimal control problems and varitional calculus using Haar wavelets. In the first chapter, we introduce general optimal control problems, varitional calculus problems, the needed definitions, Haar wavelets and using of them we solve optimal control problems. The second chapter, consists of the shortest path problems and the fourth chapter consists of the trajectory optimization problems of robot manipulators and numerical results are also given for some examples, then it is approximated using Haar wavelet. In this thesis all graphs are plotted by matlab software.