A predictor-corrector compact difference scheme is proposed for a solution of a class of nonlinear Burgers type equations. Firstly, by using the first-order Euler scheme for the first-order time derivative, the time integral term is discretized based on the first-order convolutional quadrature formula, with the two-step prediction correction acheme of the MacCormack method adopted to handle the nonlinear term. Then, a fourth order compact difference is used for the separation of the first and second derivatives of the scattered space, thus construting an Euler prediction correction compact difference fully discrete scheme. Finally, the validity of the proposed algorithm is to be verified by numerical examples.