In this article,a new class of threshold ARMA-ARCH model with random delay is proposed.Its limited behavior is discussed and the sufficient condition for its convergence is obtained.This paper makes threshold ARMA-ARCH model with fixed time delay to threshold ARMA-ARCH model with random time delay,so it can better imitate many substantial problems in the real world.On the other hand,this paper popularizes the ARCH model,which makes the model more adaptive to improve application to phenomena of price behavior fluctuation in financial market.