In order to solve the problem that the traditional trajectory planning method cannot flexibly control the velocities and the arrival time of critical points in the trajectory, this paper proposes a non-uniform rational B-spline interpolator based on double-step signal and finite impulse response filters. The interpolator consists of two modules: a pre-processing module and a real-time interpolation module. To reduce the contour error, first, the pre-processing module scans the curve for critical points and sets their velocities according to the chord error. Then, the curve is split, and for each segment, the length and inverse length functions are calculated to eliminate the length error and enhance the real-time performance. Moreover, to control the arrival time and smooth the velocity, the real-time interpolation module generates the trajectory by processing the double-step signal with three finite impulse response filters, which satisfies the constraints of velocity, acceleration, jerk, and displacement. Simulation results indicate that the proposed interpolator can accurately reach the critical points at the set arrival time with smooth velocity and low chord error, and experimental results on a SCARA robot show that the proposed interpolator is feasible and effective.