The main objective of this paper is to obtain a new accurate approximate solutions for a kind of ordinary differential equations called multipoint boundary value problems by using simple modification of optimal homotopy asymptotic method (OHAM). This procedure is a well-performance for calculating a better approximate solutions using one-order of approximation comparing with other methods which need higher order of approximations to gives the same results. Some examples are presented to testify the accuracy and applicability of this procedure. Comparisons are made between the present procedure and the other methods.