Despite the empirical success of Genetic programming (GP) in various symbolic regression applications, GP is not still known as a reliable problem-solving technique in this domain. Non-locality of GP representation and operators causes ineffectiveness of its search procedure. This study employs semantic schema theory to control and guide the GP search and proposes a local GP called semantic schema-based genetic programming (SBGP). SBGP partitions the semantic search space into semantic schemas and biases the search to the significant schema of the population, which is gradually progressing towards the optimal solution. Several semantic local operators are proposed for performing a local search around the significant schema. In combination with schema evolution as a global search, the local in-schema search provides an efficient exploration–exploitation control mechanism in SBGP. For evaluating the proposed method, we use six benchmarks, including synthesized and real-world problems. The obtained errors are compared to the best semantic genetic programming algorithms, on the one hand, and data-driven layered learning approaches, on the other hand. Results demonstrate that SBGP outperforms all mentioned methods in four out of six benchmarks up to 87% in the first set and up to 76% in the second set of experiments in terms of generalization measured by root mean squared error.