Climate forecasting plays an important role for human life in many areas such as water management, agriculture, natural hazards including drought and flood, tourism, business, and regional investment. Estimating these data is a difficult task as the time series climate parameter values vary monthly and seasonally. Therefore, predicting climate parameters based on learning and artificial intelligence is important to long-term efficient results in these fields. For this purpose, in this study, a time-series based Long Short-Term Memory (LSTM) deep neural network is proposed to predict future climate in Çankırı and Adıyaman cities in Turkey. With the help of this network, the average temperature, relative humidity, and precipitation values, which are known as the most effective climate parameters, have been estimated. An improved Particle Swarm Optimization (PSO) technique is also proposed to optimize input weight values of the LSTM deep network, and reduce the estimation errors. The proposed algorithm is compared with deep models of LSTM variants based on Root Mean Square Error (RMSE), Mean Absolute Deviation (MADE), and Mean Absolute Percentage Error (MAPE) metrics. The proposed adaptive LSTM-PSO and non-adaptive LSTM-PSO models achieved at RMSE 0.98 and 1.05 for temperature, 1.19 and 1.27 for relative humidity, and 4.21 and 4.67 for precipitation estimation, respectively. The RMSE is %7 lower with the proposed adaptive LSTM-PSO method than proposed non-adaptive LSTM-PSO method.