Abstract: Let p : X → B be a smooth and projective family of Calabi-Yau 3-folds. Assuming a comparison conjecture between the nc-Hodge structures with classical Hodge structures, we prove that the categorical enumerative invariants associated to this family satisfy Bershadsky-Cecotti-Ooguri-Vafa’s holomorphic anomaly equation. This provides strong evidence that the categorical enumerative invariants may be taken as a definition of the B-model non-perturbative topological string partition function. Along the way, we also prove the dilaton, string and divisor equations hold in the context of categorical enumerative invariants.