The prediction of whether a software change is fault inducing or not in the software system using various learning methods, such study concerned in Just-In-Time Software Fault Prediction (JIT-SFP). Building such predicting model requires adequate training data. However, there is a lack of training data at the beginning of the software system. Cross-Project (CP) setting can subjugate this challenge by employing data from different software projects. It can achieve similar predictive performance as compared to Within-Project (WP) fault prediction. It is undiscovered to what level the CP training data can be useful in such a situation. It is also undiscovered whether CP data are helpful in the initial phase of fault detection, and when there is an inadequate WP train set, CP could be beneficial to extend. This article deals with such investigations in real software projects. We proposed a new method by levering a deep belief network and long short-term memory called JITCP-Predictor. Out of ten, the proposed model significantly outperforms on every ten projects over benchmark methods, and it is superior from 10.63% to 136.36%, and 7.04% to 35.71% in terms of MCC and F-measure, respectively. The mean values of MCC and F-measure produced by JITCP-Predictor is 0.52 ± 0.021 and 0.76 ± 0.76, respectively. We also found the proposed model is more suitable for large and moderate size projects. The proposed model avoids class imbalance and overfitting problems and takes reasonable training costs.