Video click-through rate (CTR) prediction is one of the important tasks in the context of video recommendation. According to click-through prediction, recommendation systems can adjust the order of the recommended video sequence to improve the performance of video recommendation. In recent years, with the explosive growth of videos, the problem of video cold start has become more and more serious. Aim for this problem, a novel video click-through prediction model is proposed which utilizes both the video content features and context features to improve CTR prediction; a simulation training of the cold start scenario and neighbor-based new video replacement method are also proposed to enhance the model's CTR prediction ability for new videos. The proposed model is able to predict CTR for both old and new videos. The experiments on two real-world video CTR datasets (Track_1_series and Track_2_movies) demonstrate the effectiveness of the proposed method. Specifically, the proposed model using both video content and contextual information improves the performance of CTR prediction for old videos, which also outperforms the existing models on both datasets. Additionally, for new videos, a baseline model without considering the cold start problem achieves an AUC score of about 0.57. By contrast, the proposed model gives much better AUC scores of 0.645 and 0.615 on Track_1_series and Track_2_movies, respectively, showing the better robustness to the cold start problem.