Vortex shedding from an oscillating circular cylinder was numerically investigated at Re = 100 using the Navier-Stokes equations and the new far-boundary stream-function condition. The detailed shedding patterns are delineated by means of the streakline plotting and the lift-coefficient curves. A parameter map is presented that distinguishes synchronized from asynchronous shedding and double-vortex from single-vortex shedding. The computational result is in good qualitative agreement with earlier experimental results.