New forms of trapping force are proposed for the design of near-field optical tweezers. Without the limitation of dipole approximation, the trapping force acting on a nano-particle located in near-field region can be solved by direct calculation of Maxwell stress tensor using 3D FDTD method. The new forms are used to design near-field optical trapping with a metal-coated fiber probe. Calculations show that the fiber probe can trap a nano-particle with tens of nanometres diameter to different positions with different distance from the probe tip. In order to achieve higher trapping capability, the feasibility of near-field trapping near the optical fiber probe after adding the AFM metallic probe is shown by analyzing trapping forces along three axis directions. The correctness of new forms is demonstrated by numerical results.