An approach for robot plane curve trajectory planning was proposed, which satisfies the mixed constraints in both Cartesian space and joint-variable space. In the Cartesian space, the determination of control knot points, the time assignment among the knots, and the deviation estimation between the planned trajectory and the desired trajectory were discussed. And in the joint-variable space, cubic spline polynomials fitting to the segment between two adjacent knots were discussed and the methods to satisfy the joint physical constraints (the velocity, acceleration, and torque constraints) were studied. According to the deviation between the planned trajectory and the desired trajectory, knot points were inserted unevenly among the predetermined knots. Thus the deviation was decreased significantly by adding small number of knots. At last, an algorithm for plane curve trajectory planning was presented in detail. A typical industrial robot trajectory planning example was given to demonstrate the effectiveness of this method.