Parallel time integration methods provide the time integral simulation with parallelism in time direction and enhance the performance of the applications on parallel machines. Many parallel time integration methods apply re-discretization with enlarged time step width to propagate prior time step information to later time steps with low calculation cost. However, this re-discretization tends to create an unstable time integral problem and causes the performance degradation depending on the length of the time step width. Therefore, we paid attention to the correction scheme involved in the (parallel) TP-EEC method that uses Jacobian matrices of original simulation problem to propagate the prior time step information to later time steps very quickly. This paper showed our parallel time integration approach using a correction method similar to the TP-EEC method, and proposed the efficient implementation methods with pipeplined coarse level correction. The performance results for simple non-linear time step simulation show our method performed well and was faster than other representative parallel time integration scheme.