Some finite-difference methods, which use primitive variables, are proposed to analyze an incompressible fluid flow. Especially, two methods are developed: one is to calculate the accurate pressure field immediately after the fluid starts to flow (two-step method); the other allows a larger time-step than the corresponding explicit method (non-iterative implicit method). As a numerical example, the two-dimensional transient Womersley flow, and the non-iterative implicit method requires less computer time compared with the explicit method.