In this paper, we focus minimum time optimal problems which have output and output-derivative constraints and propose a closed loop system design with “Optimal Look-up-Table (OLT) Controller” based on Genetic Algorithm. The OLT Controller uses an OLT as an upper or a lower bounds of an input which is produced by a feedback controller (PI controller). If the input is within the bounds, the suggested OLT controller works as same as the feedback controller; if the input is without the bounds, the OLT controller gives the optimal control according to the OLT. Thus, this approach would generate a sub-optimal but practical control.