Handwritten character recognition (HCR) is a growing field in the applications of pattern recognition, image processing, communication technologies, and so on. But, the identification of handwritten characters affected because of different styles of writers, or even one writer's style differed according to the conditions. Moreover, the huge amount of features from the handwritten characters also affect the classification. To address the aforementioned issues, the hybrid feature extraction (HFE) with morlet stacked sparse auto-encoder (MSSAE) based feature dimensionality reduction is proposed for improving the classification of HCR. Here, the HFE is the combination of different textural and shape features such as histogram of oriented gradients (HOG), gray-level co-occurrence matrix (GLCM), discrete wavelet transform (DWT), and skeleton features. The morlet wavelet activation function is used in the MSSAE to enhance the dimensionality reduction ability that used for an effective reduction of feature dimensions. The reduction of feature dimension using MSSAE is used to improve the classification using multi-class support vector machine (MSVM). In this research, the real-time indigenous languages i.e., English and Kannada handwritten characters from the Chars74K dataset are used for the analysis i.e., offline recognition. On the other hand, the online recognition of Kannada characters is also done for analyzing the HFE-MSSAE method. The HFE-MSSAE method is analyzed in terms of accuracy, precision, recall, CSI and F-measure. The existing researches namely convolutional neural network (CNN), hybrid feature based long short term memory (HF-LSTM) and elephant herding optimization -long short term memory (EHO-LSTM) are used to evaluate the HFE-MSSAE method. The accuracy of the HFE-MSSAE for Kannada is 96.73% which is higher than the HF-LSTM and EHO-LSTM.