The process of algal bloom evolution in rivers or lakes has characteristics of suddenness and uncertainty, which leads to low prediction accuracy of algal bloom. To solve this problem, chlorophyll a concentration was used as the surface index of cyanobacteria bloom evolution process, and a cyanobacterial bloom forecast model based on Long Short-Term Memory (LSTM) and Recurrent Neural Network (RNN) was proposed. Firstly, the improved Genetic algorithm-First order lag filter (GF) optimization algorithm was taken as data smoothing filter. Secondly, a GF-LSTM network model was built to accurately predict the cyanobacterial bloom. Finally, the data sampled from Meiliang Lake in Taihu area were used to test the forecast model, and then the model was compared with the traditional RNN and LSTM network. The experimental results show that, the mean relative error of the proposed GF-LSTM network model is 16%-18%, lower than those of RNN model (28%-32%) and LSTM network model (19%-22%). The proposed model has good effect on data smoothing filtering, higher prediction accuracy and better adaptability to samples. It also avoids two widely known issues of gradient vanishing and gradient exploding when using traditional RNN model during long term training.