A rapid convergence method for calculating all induced velocity components by contracted vortex lines(e.g., tip vortex and inboard vortex) is presented. The advantage of the method is, the induced velocities at any point in the wake can be calculated and the wake contraction is considered. Not only does it avoid the truncation errors associated with discretization of the vortex lines, but also reduces integrand errors corresponding to finite azimuthal angle. Therefore, both numerical precision and integrand convergence rate are obviously improved. This method is developed from Rand and Chiu's method(a rapid convergence method for computing the induced velocity by a helical vortex line), which is based on finding upper and lower bounds on the truncated integral.