CRM is at the core of any customer-focused business strategy and includes the people, processes, and technology questions associated with marketing, sales, and service. In today's hyper-competitive world, organizations looking to implement successful CRM strategies need to focus on a common view of the customer using integrated information systems and contact center implementations that allow the customer to communicate via any desired communication channel. A CRM solution contains a number of sophisticated tools that enable to extract detailed information about customers. This information can be used to gain a better understanding of customers. From this we can determine trends, and so refine business toward customers' needs and target new products to particular customer groups. This paper presents an approach for forming the product-customer groups using neural networks for customer relationship management. The Carpenter-Grossberg's neural network, which has been used for manufacturing cell formation in group technology, is modified and applied for product-customer group formation. As a result of numerical experiments, it is also useful for more complex problems in which customers have different preferences for each product.