Nowcasting of convective weather is a challenging and significant task in operational weather forecasting system. In this study, a new convolution recurrent neural network (ConvRNN)-based regression network for convective weather prediction is proposed, which is named as the Convective Weather Nowcasting Net (CWNNet). The CWNNet adopts the joint observations of Fengyun-4A geostationary satellite and the ground-based Doppler weather radar data of the last 0-1-hour as the inputs of the model to predict the radar reflectivity factor maps of next 0-1 hour. The statistical validating results clearly demonstrate that the mean values of the probability of detection , false alarm ratio , threat score, root mean square error and mean absolute error evaluating the performance of CWNNet for 1-h nowcasting reach 0.87, 0.137 , 0.71, 3.365 dBZ and 1.038 dBZ, respectively. Due to that the geostationary meteorological satellite is capable of capturing the features of convective initiation, the CWNNet shows a good performance in convective initiation nowcasting. Besides, several case studies also further indicate that the CWNNet can predict convective initiation more than 30 minutes in advance by monitoring the convective clouds. The CWNNet based on the joint satellite and radar data shows a better nowcasting performance than that only employing single data source. Thus, it can effectively produce more reliable nowcasting for convective weather events.