For series cascade processes with a time delay, such as the first-order with time-delay (FOTD) process, the integral with time-delay (ITD) process, second-order integral with time-delay (SOITD) process, and unstable first-order with time-delay (UFOTD) process, this paper proposes a Smith-predictor-based design of analytical PI-PD control for these series cascade processes with a time delay. Firstly, targeting the common FOTD model in the secondary loop, a controller with a PID structure is designed using the direct synthesis method. Additionally, a Smith-predictor-based PI-PD control structure is adopted for the prevalent process model in the primary loop. Then, expressions representing the relationship between the corresponding controller parameters and the maximum sensitivity (Ms) index are established to facilitate the analytical design of the controllers. Finally, based on simulation experiments, the effectiveness and superiority are validated by using the proposed method.