The application of a finite element scheme to full three-dimensional incompressible viscous flow around an impulsively started circular cylinder is presented in this paper. The scheme is based on the Petrov-Galerkin weak formulation with exponential weighting functions. The incompressible Navier-Stokes equations are numerically integrated in time by using a fractional step strategy with second-order accurate Adams-Bashforth scheme for both advection and diffusion terms. Numerical results demonstrate the workability and the validity of the present approach.