Due to the unavoidable various time delays among the controllers, actuators and sensors in mechatronic systems, which are typically caused by establishing stale communications or time-consuming computations, the closed-loop systems with these delay effects exhibit overshooting, oscillations, and degenerated control accuracy. Conventional methods often focus on the stability analysis of control design with a time delay in the continuous time domain and rarely pay close attention to its digital realization in practical systems. This manuscript proposes a novel control strategy based on the super-twisting algorithm (STA) as the second-order sliding mode control (SMC) with the time delay compensated by a modified Smith predictor (MSP). To reduce the numerical chattering, the STA-MSP is discretized and realized by a semi-implicit Euler method, which makes the STA-MSP insensitive to gain overestimation and large iteration periods of closed-loop control. Simulation and experimental results demonstrate that the proposed STA-MSP realization method achieves high performance in terms of control accuracy when there exists a known constant time-delay between the controller and the actuator.