The anomalous Hall conductivity (AHC) and anomalous Nernst conductivity (ANC) are two prominent transport phenomena in ferromagnetic materials of a topological nature. Based on first-principles calculations, we evaluated the AHC and ANC of 35 cubic ferromagnetic antiperovskites (APVs) and observed giant AHC and ANC as large as 1128 S/cm and 6.27 AK-1m-1 for Co3LiN and Co3PtN, respectively. Detailed analysis reveals that the origin of giant ANC can be attributed to the occurrence of Weyl nodes near the Fermi energy, as demonstrated for Co3PtN. Interestingly, both the magnitude and sign of AHC and ANC can be tuned by changing the magnetization (M) directions, which could be applied to realize spin-caloritronics devices.