The five-parameter logistic minus one-parameter model is a hybrid between the five-parameter model and the four-parameter model used for the relationship between concentration and response. The four-parameter model includes the maximum and minimum concentration, slope, and the median concentration level EC50. The five-parameter model add an asymmetric factor which is important due to asymmetry of the sigmoid curve. This model, however, is more difficult to fit due to the addition of the fifth parameter, which is why the 5PL-1P model is used so that the asymmetric factor is taken into account but has less parameters. For the 5PL-1P model, D-optimal designs are obtained to estimate the model parameters effectively. Then we compare the D-optimal designs to the designs that are used to study the 5PL-1P model in real toxicity assessment and show that they work better than the original designs by comparing their efficiencies and comparing MSEs through simulation studies.