This paper studies a novel recurrent neural network (RNN) with hyperbolic secant (sech) in the gate for a specific medical application task of Parkinson’s disease (PD) detection. In detail, it focuses on the fact that patients with PD have motor speech disorders, by converting the voice data into black-and-white images of a recurrence plot (RP) at specific time intervals and constructing the detection model that combines RNN and convolutional neural network (CNN); the study evaluates the performance of the RNN with sech gate compared with long short-term memory (LSTM) and gated recurrent unit (GRU) with conventional gates. As a result, the proposed model obtained similar results to LSTM and GRU (an average accuracy of about 70%) with less hyperparameters, resulting in faster learning. In addition, in the framework of the RNN with sech in gate, the accuracy obtained by using tanh as the output activation function is higher than using the relu function. The proposed method will see more improvement by increasing the data in the future. More analysis on the input sound type, the RP image size, and the deep learning structures will be included in our future work for further improving the performance of PD detection from voice.