The Susceptible-Exposed-Infectious-Recovered (SEIR) model serves as a pivotal tool in simulating infectious diseases like COVID-19, offering a structured framework to analyze how diseases spread through populations over time. It allows researchers and policymakers to estimate key epidemiological parameters such as transmission rates, incubation periods, and recovery rates, crucial for designing effective public health interventions. This study implements multistep block method with predictor and corrector scheme to approximate the population representing individuals who are susceptible to the disease, those that exposed to the disease, those who has infected, and also those who has recovered from the disease. The multistep method is derived by using Lagrange interpolation and the two-points solutions are obtained simultaneously in block method. These two solutions are then iterated by using predictor-corrector scheme to improve the accuracy of the approximate solutions. The proposed method then tested to solve the SEIR model and compared with the established previous methods to observe its accuracy performance. The factors contributed to its computational time required such as total steps and total function calls also discussed and compared with previous method. Overall, the research contributes a robust computational framework for SEIR modeling, advancing capabilities to simulate and understand disease spread dynamics effectively.