Acoustic propagation delay has not been investigated for a continuous wave multistatic sonar tracking system except for the recent study conducted by Jauffret et al. [6], which estimates the trajectory of a constant velocity target. The results showed that the estimate bias caused by the propagation delay is not negligible, especially for a bistatic system. This paper develops an interacting multiple model unscented Gauss-Helmert filter with numerical Jacobian (IMM-UGHF-NJ) to track a maneuvering target with propagation delay using a bistatic sonar system. The IMM-UGHF-NJ can overcome the two tracking challenges introduced by the delay, namely, implicit state transition model and lack of analytical expression of the Doppler shifted frequency in the measurement model. Simulation tests have been conducted, and the results show that the IMM-UGHF-NJ can reduce the estimation error significantly, especially for long range or fast moving targets.