Hydrodynamic properties of squirmer swimming in power-law fluid near a wall considering the interaction between squirmer and wall are numerically studied with an immersed boundary-lattice Boltzmann method. The power-law index, Reynolds number, initial orientation angle of squirmer, and initial distance of squirmer from the wall are all taken into account to investigate the swimming characteristics for pusher (<0), neutral squirmer (=0), and puller (>0) (three kinds of swimmer types) near the no-slip boundary. Four new kinds of swimming modes are found. Results show that, for the pushers and pullers, the wall displays an increasing attraction with increasing power-law index n, which differs from the neutral squirmer who always departs from the wall after the first collision with the wall. Both the initial orientation angle and initial distance from the wall only affect the moving situations rather than the moving modes of the squirmers. However, the squirmers depart from the wall as the Reynolds number increases and chaotic orbits appear for some squirmers at Re=5. Several typical flow fields are analyzed and the power consumption and torque for different kinds of flows are also studied. It is found that, as the absolute value of increases, the power consumption generally increases in shear-thinning (n=0.4), Newtonian (n=1), and shear-thickening (n=1.6) fluids. Moreover, the pushers (<0) and the pullers (>0) expend almost the same power if the absolute value of remains the same. In addition, the power consumption of the squirmers is highly dependent on the power-law index n.