The aim of this book is to present a method for solution of system of first order initial value problems of ordinary differential equation by a semi -analytic technique with constructing polynomial solutions . The original problem is concerned using two -point o sculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] and give some examples illustrate suggested method and accuracy, easily implemented. The accuracy of the method is confirmed by compared with conventional methods ( RK4, RK -Butcher , DTM , HPM , ABM ) .The existence , uniqueness and sensitivity of solutions to the system of ordinary initial value problems is discussed . Also, introduce some general observations about control of a residual and control of the local error and develop inexpensive estimates of both the local error and the size of the residual. Then develop an effective program to solve the system of ordinary initial differential equations . Finally , give some applications about the system of ordinary initial value problems