This paper shows that the performance of a nonlinear fluid engine mount can be improved by an optimal design process. The property of a hydraulic mount with inertia track and decoupler differs according to the disturbance frequency range. Since the excitation amplitude is large at low excitation frequency range and is small at high excitation frequency range, mathematical model of the mount can be divided into two linear models. One is a low frequency model and the other is a high frequency model. The combination of the two models is very useful in the analysis of the mount and is used for the first time in the optimization of an engine mount in this paper. Normally, the design of a fluid mount is based on a trial and error approach in industry because there are many design parameters. In this study, a nonlinear mount was optimized to minimize the transmissibilities of the mount at the notch and the resonance frequencies for low and high-frequency models by a popular optimization technique of sequential quadratic programming (SQP) supported by $MATLAB^{(R)}$subroutine. The results show that the performance of the mount can be greatly improved for the low and high frequencies ranges by the optimization method.