Public cultural services for the elderly are part of the government-led public services for society in order to meet the needs of people’s spiritual and cultural life. As the global problem of ageing becomes increasingly serious, the problem of balancing the supply and demand of public cultural services for the elderly has become increasingly serious. How to realize a public cultural service system for the elderly with wide coverage and effective integration of resources has become a pressing problem to be solved. In order to solve the above problems, this article designs a public cultural service system for the elderly based on intelligent computing. Firstly, the problems that lead to the inefficient use of public cultural resources for the elderly are analyzed. Secondly, it attempts to introduce an advanced intelligent computing technology (Cuckoo Search) to build a three-dimensional public cultural resource sharing system for the elderly. Then, the standard Cuckoo algorithm is improved by using chaotic mapping and dynamic step size for the characteristics of public cultural services in order to improve the convergence speed and the accuracy of the search. The experimental results show that the designed system can effectively integrate the grassroots resources of cultural institutions such as libraries, cultural centres, and cultural service centres, verifying its effectiveness and feasibility.