A modified SIMPER algorithm is developed for analysis of microfluid effects on the motion and deformation of a red blood cell (RBC) in a capillary. With consideration of very small Reynolds number in microfluidics, this algorithm not only speeds up the convergence of the momentum equations by combining the advantages of the SIMPLEC and SIMPLER algorithms together, but also satisfies the continuity equation with higher accuracy by integrating a fine adjustment technique. In order to validate the modified SIMPLER algorithm, the behavior of RBC in a capillary is simulated at different velocities. When the mean RBC velocity is 0.1mm/s, the RBC exhibits a characteristic parachute shape in the steady state, which agrees well with the numerical results previously reported. Apart from that, a quantitative validation with the experimental data is performed by examining the relationship between the mean velocity and deformation index of the RBC, showing an excellent agreement. The effects of crucial parameters are investigated systematically on the motion and deformation of the RBC, including the RBC radius, elastic modulus and bending stiffness of RBC membrane, initial velocity of suspending fluid, as well as the density and viscosity ratios of the suspending fluid to RBC. The simulation results demonstrate that all of the parameters have influences on the RBC behavior by changing the interaction between the RBC and suspending fluid.