Abstract: Microorganisms are one of the important parts of natural ecosystem, understanding the kinematic behaviors of microorganisms swimming in complex fluids could provide guidance for the design and manufacturing of MEMS. Wall effects are one of the most important scientific problems of the research of microorganism swimming, and recent work reveals that microorganisms show complicated swimming behaviors near the wall. However, most of the work reported in the literatures focused on microorganism swimming in Newtonian fluid, less attention is paid on microorganism swimming in viscoelastic fluid or other non-Newtonian fluids. A direct-forcing fictitious domain method combined with Cholesky decomposition for the simulation of microorganisms swimming in a viscoelastic fluid is reported in this paper. The squirmer model is applied to represent the swimming of microorganisms. The numerical schemes for the discretization of Giesekus constitutive equation are first presented and validated. The newly developed simulation model is then applied to investigate the effect of planar wall on swimming dynamics of current squirmer in viscoelastic flow, i.e., Giesekus fluid. The results show that the swimming direction of squirmer is a critical factor of the wall-trapping effect. The fluid elasticity affects the swimmer motion near solid wall by generating an elastic torque which reorient the swimming direction. The time for the squirmer to contact planar wall in viscoelastic fluid is almost twice of that in Newtonian fluid.