This paper considers the model averaging prediction in a quasi-likelihood framework that allows for parameter uncertainty and model misspecification. We propose an averaging prediction that selects the data-driven weights by minimizing a K-fold cross-validation. We provide two theoretical justifications for the proposed method. First, when all candidate models are misspecified, we show that the proposed averaging prediction using K-fold cross-validation weights is asymptotically optimal in the sense of achieving the lowest possible prediction risk. Second, when the model set includes correctly specified models, we demonstrate that the proposed K-fold cross-validation asymptotically assigns all weights to the correctly specified models. Monte Carlo simulations show that the proposed averaging prediction achieves lower empirical risk than other existing model averaging methods. As an empirical illustration, the proposed method is applied to credit card default prediction.