A kinematics model-free trajectory tracking method for a robotic arm includes the following steps. Obtain an actual trajectory equation ra(t) of the robotic arm at time t according to a sensor, and combines the actual trajectory equation ra(t) with a predetermined target trajectory equation rd(t) to obtain a first error function e(t). Obtain a differential equation (I) of a state change rate of a driver of the robotic arm. Obtain a second error function ε(t). Pass the second error function c(t) through the applied gradient neural network to obtain equation (IV). Jointly solve equation (I) and equation (IV) to obtain an joint state vector θ(t) of the robotic arm. Drive a motion of the robotic arm by a controller according to the joint state vector θ(t) of the robotic arm to complete trajectory tracking.