In order to improve the large anomalous Hall effect (AHE) in Mn3Sn thin films, we eliminated the co-existing Mn2Sn phase in the films by changing the composition; 50 nm thick polycrystalline Mn3+ x Sn thin films were fabricated on Si/SiO2 substrates by the sputtering method followed by a thermal annealing process in vacuum. The film compositions were Mn70Sn30(sample-A), Mn75Sn25(sample-B), and Mn80Sn20(sample-C) in as-deposited state and were slightly changed to be Mn75Sn25(sample-A), Mn77Sn23(sample-B), and Mn78Sn22(sample-C), respectively, after the annealing at 500 °C. From a structural analysis by X-ray diffractometry, the sample-C was considered to crystallize to Mn3Sn phase without passing the crystallization of Mn2Sn phase at 300 °C, differently from the sample-A. The saturation magnetization, $M_{\mathrm {S}}$ , of the sample-A significantly increased below 250 K, corresponding with the Curie temperature of Mn2Sn. On the other hand, $M_{\mathrm {S}}$ did not show significant changes with cooling temperature in the samples-B and -C. An AHE was observed at the room temperature in all the samples. The anomalous Hall conductivity, $\sigma _{\mathrm {AH}}$ , at the room temperature increased in magnitude, as the content of Mn increased. The sign of $\sigma _{\mathrm {AH}}$ changed from negative to positive in the sample-A with cooling temperature. On the other hand, the sign remained negative in the sample-C. These differences might be due to the elimination of co-existing Mn2Sn phase in the Mn3Sn thin films with enlarging the Mn content from the stoichiometry. Consequently, we successfully improved the large AHE in polycrystalline antiferromagnetic Mn3Sn thin films.