Monte Carlo orbit-following simulations based on a phase-space coordinate transform method are presented in this paper. Guiding-center orbits are computed by using this method, that is, using the phase-space coordinate transform and solving the gyrokinetic equations of motion. This method has been adopted in a Monte Carlo orbit-following code GYCAVA for studying the behavior of fast ions in a tokamak. The finite Larmor radius effect can be included in the guiding-center orbit computation. The cylindrical coordinates are used for avoiding singularity of the safety factor at X points of the divertor configuration. An n-point discrete sum method is used to compute the gyro-average, which is related to the finite Larmor radius effect. The GYCAVA code has been integrated with other equilibrium, magnetohydrodynamic and neutral beam injection codes for studying losses and wall loads of fast ions in the presence of perturbation fields. The GYCAVA code has been verified by tests of the orbit computation and the Monte Carlo Coulomb collision. Simulations of fast ion losses in the presence of resonant magnetic perturbations in the EAST tokamak have been performed.