Accurate short-term precipitation forecast is extremely important for urban flood warning and natural disaster prevention. In this paper, we present an innovative deep learning model named ISA-PredRNN (improved self-attention PredRNN) for precipitation nowcasting based on radar echoes on the basis of the advanced PredRNN-V2. We introduce the self-attention mechanism and the long-term memory state into the model and design a new set of gating mechanisms. To better capture different intensities of precipitation, the loss function with weights was designed. We further train the model using a combination of reverse scheduled sampling and scheduled sampling to learn the long-term dynamics from the radar echo sequences. Experimental results show that the new model (ISA-PredRNN) can effectively extract the spatiotemporal features of radar echo maps and obtain radar echo prediction results with a small gap from the ground truths. From the comparison with the other six models, the new ISA-PredRNN model has the most accurate prediction results with a critical success index (CSI) of 0.7001, 0.5812 and 0.3052 under the radar echo thresholds of 10 dBZ, 20 dBZ and 30 dBZ, respectively.