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We study the quasi-two-body decays B→PD∗0(2400)→PDπ with P=(π,K,η,η′) in the perturbative QCD factorization approach. The predicted branching fractions for the considered decays are in the range of 10-9-10-4. The strong Cabibbo-Kobayashi-Maskawa (CKM) suppression factor RCKM≈λ4(̄ρ²+̄η²)≈3×10-4 results in the great difference of the branching ratios for the decays with D∗0 and ̄D∗0 as the intermediate states. The ratio R̄D*00 between the decays B0→̄,D*00K0→D-π+K0 and B0→̄D*00π0→D-π+π0 is about 0.091+0.003-0.005, consistent with the flavor-SU(3) symmetry result. The ratio for the branching fractions is found to be 1.10+0.05-0.02 between B(B0s→D*+0K-→D0π+K-) and B(B0→D*+0π-→D0π+π-) and to be 1.03+0.06-0.07 between B(B0s→̄D*00̄K0→D-π+̄K0) and 2B(B0→̄D*00π0→D-π+π0). The predictions in this work can be tested by the future experiments. [ABSTRACT FROM AUTHOR]