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In this paper, an unconditionally stable finite- difference time-domain (FDTD) method in cylindrical coordinates is developed to analyze electromagnetic responses under axially symmetric measure-while-drilling/logging-while-drilling (MWD/LWD) environments. The method is based on the application of the Crank-Nicholson scheme to the FDTD method in cylindrical coordinates. To accelerate the solution of this approach, an algebraic multigrid method is applied. For several MWD/LWD electromagnetic simulations, it is observed that the proposed method can be close to 20 times faster than the conventional FDTD method.