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Abstract Searching for topological superconductors that host topological charge-neutral Majorana zero-modes at edges has become a central problem in condensed matter research due to their potential applications for quantum computations. Meanwhile, electron correlations in solid-state materials enhance quantum fluctuations and give rise to various quantum many-body phases. Whether these electron correlations alone would lead to topological superconductivity is a fundamentally important open problem. Here, we theoretically find the correlation-driven topological superconductivity in a class of Kondo lattice materials. Therein, the odd-parity Kondo hybridization mediates ferromagnetic spin-spin coupling and leads to spin-triplet pairing between local moments. Triplet $$p\pm i{p}^{{\prime} }$$ p ± i p ′ -wave topological superconductivity with Majorana zero modes at edges is reached when Kondo hybridization co-exists with the triplet pairings. Our results offer a detailed understanding of the experimental observations on UTe2, a ferromagnetic heavy-electron triplet superconductor. Our approach to topological superconductivity shows advantages over the heterostructure approach by proximity effect.