In today’s society, calligraphy, which reflects one’s basic writing skills, is becoming more and more important to people. People are influenced by calligraphy in their studies, work, etc. Improving calligraphy writing skills has become one of the key directions for developing one’s abilities at this stage. As an important means of improving writing skills, calligraphy practice products are attracting more and more attention and purchases. In particular, in recent years, as the market economy has developed in a deeper direction, people’s demand for calligraphy practice products has diversified and calligraphy practice product companies have launched a variety of products to meet the public’s calligraphy practice needs in order to adapt to the reality of consumer demand. However, with the development of the Internet culture industry and influenced by objective factors such as school holidays and seasons, the current market demand for calligraphy practice products is rapidly and dynamically changing, making market changes difficult to grasp and leading to poor sales, which directly affects the profits of calligraphy practice product-related companies. The artificial intelligence neural network method realizes the nonlinear relationship between the input and output of sample data through the self-learning ability of each neuron and has a certain nonlinear mapping ability in prediction, which plays a great role in the market demand prediction of many commercial products. Based on this, this paper proposes a recursive neural network-based algorithm to predict the future demand and development trend of calligraphy practice products through extensive and in-depth research, so as to provide positive and beneficial guidance for enterprises’ future production and sales.