Tibetan script possesses a distinctive artistic form of writing, intricate glyph structures, and diverse stylistic variations. In the task of text recognition, effectively handling the recognition of Tibetan script with significantly different stylistic fonts remains a challenge. Existing research has made considerable progress in recognizing Tibetan script within a single style using techniques such as convolutional neural networks and convolutional recurrent neural networks. However, when dealing with multi-style Tibetan script recognition, the standard approach involves training models using a multi-label joint training method. This approach annotates the style and class of different font style samples and merges them into a single dataset for model training. Nevertheless, as the amount of data and performance requirements increase, this approach gradually faces issues such as decreasing accuracy, insufficient generalization capability, and poor adaptability to new style samples. In this paper, we propose a transfer learning-based method for incremental recognition of multi-style Tibetan script, referred to as "multi-style Tibetan script incremental recognition." This method learns and completes the recognition of new style Tibetan script gradually from models that already possess recognition capabilities for a specific style. The proposed method consists of the following stages: 1) A multi-style classifier based on the VGG-16 network is designed to extract features that enable precise differentiation between different font styles of Tibetan script; 2) A pre-training phase is conducted using a residual network on the Tibetan script's standard Uchen style, resulting in an efficient feature extractor and a classifier capable of effectively recognizing the standard style, serving as a baseline model; 3) Through transfer learning, the feature extraction part of the baseline model is frozen, forming a shared feature extractor used for feature extraction of Tibetan script in the Uchen variant and antiquarian character styles. Corresponding classifiers are trained based on different styles; 4) By combining the multistyle classifier, shared feature extractor, and category classifier, recognition of Tibetan script characters is achieved. This method incrementally recognizes new styles based on the existing recognition model for Tibetan script in the Uchen standard style. Experimental results demonstrate that this method enhances the recognition accuracy of Tibetan script in Uchen standard, variant, and antiquarian character styles to 99.04%, 98.05%, and 97.66% respectively, using the TCDB and HUTD datasets. Compared to the traditional multitask recognition approach, the overall recognition accuracy improved from 90.14% to 98.40%. This method exhibits high accuracy, strong generalization capability, and good adaptability to new style samples in multistyle Tibetan script character recognition. Furthermore, it can be applied to other tasks involving multi-style, multi-font, and multi-script recognition.