We investigate the phase field equation coupled with the Navier-Stokes equation that describes the cell and blood flow. We use the finite element method to simulate the process of the cell going through a capillary. The phase-field equation, which is a fourth-order problem, is transformed into two decoupled Helmholtz-type equations using a stabilizer. The Navier-Stokes equation is computed by the concept of inexact factorization. It is proved that the first-order semi-implicit schemes are energy stable under some conditions. We adopt the second-order schemes to compute the model for considering the high accuracy, which are also energy stable from the numerical cases. We simulate the system on an irregular domain and obtain the numerical results,which demonstrate that it is more difficult for a large cell to pass through the capillary than it is for a small one.