We carried out three-dimensional magnetohydrodynamic simulations to study the effects of plasma viscosity on the formation of sharp discontinuities of density and temperature distributions, cold fronts, in clusters of galaxies. By fixing the gravitational potential that confines the cool, dense plasma in a moving subcluster, we simulated its interaction with the hot, lower density plasma around the subcluster. At the initial state, the intracluster medium (ICM) is assumed to be threaded by uniform magnetic fields. The enhancement of plasma viscosity along the direction of magnetic fields is incorporated as anisotropic viscosity depending on the direction of magnetic fields. We found that the Kelvin-Helmholtz instability at the surface of the subcluster grows even in models with anisotropic viscosity, because its effects on the velocity shear across the magnetic field lines are suppressed. We also found that magnetic fields around the interface between the subcluster and ICM are amplified even in the presence of viscosity, while magnetic fields behind the subcluster are amplified up to beta(-1) similar to 0.01 in models with viscosity, whereas they are amplified up to beta(-1) similar to 0.1 in models without viscosity, where beta is the ratio of gas pressure to magnetic pressure.