The diversified service requirements in vehicular networks have stimulated the investigation to develop suitable technologies to satisfy the demands of vehicles. In this context, network slicing has been considered as one of the most promising architectural techniques to cater to the various strict service requirements. However, the unpredictability of the service traffic of each slice caused by the complex communication environments leads to a weak utilization of the allocated slicing resources. Thus, in this paper, we use Long Short-Term Memory- (LSTM-) based resource allocation to reduce the total system delay. Specially, we first formulated the radio resource allocation problem as a convex optimization problem to minimize system delay. Secondly, to further reduce delay, we design a Convolutional LSTM- (ConvLSTM-) based traffic prediction to predict traffic of complex slice services in vehicular networks, which is used in the resource allocation processing. And three types of traffic are considered, that is, SMS, phone, and web traffic. Finally, based on the predicted results, i.e., the traffic of each slice and user load distribution, we exploit the primal-dual interior-point method to explore the optimal slice weight of resources. Numerical results show that the average error rates of predicted SMS, phone, and web traffic are 25.0%, 12.4%, and 12.2%, respectively, and the total delay is significantly reduced, which verifies the accuracy of the traffic prediction and the effectiveness of the proposed strategy.