We present a stellar mass-metallicity relation at z similar to 1.4 with an unprecedentedly large sample of similar to 340 star-forming galaxies obtained with Fibre Multi-Object Spectrograph (FMOS) on the Subaru Telescope. We observed K-band selected galaxies at 1.2 < z(ph) < 1.6 in the Subaru XMM-Newton Deep Survey/Ultra Deep Survey fields with M-* >= 10(9.5) M-circle dot, and expected F(H alpha) >= 5 x 10(-17) erg s(-1) cm(-2). Among the observed similar to 1200 targets, 343 objects show significant H alpha emission lines. The gas-phase metallicity is obtained from [N ii] lambda 6584/H alpha line ratio, after excluding possible active galactic nuclei. Due to the faintness of the [N ii] lambda 6584 lines, we apply the stacking analysis and derive the mass-metallicity relation at z similar to 1.4. Our results are compared to past results at different redshifts in the literature. The mass-metallicity relation at z similar to 1.4 is located between those at z similar to 0.8 and z similar to 2.2; it is found that the metallicity increases with decreasing redshift from z similar to 3 to z similar to 0 at fixed stellar mass. Thanks to the large size of the sample, we can study the dependence of the mass-metallicity relation on various galaxy physical properties. The average metallicity from the stacked spectra is close to the local Fundamental Metallicity Relation (FMR) in the higher metallicity part but greater than or similar to 0.1 dex higher in metallicity than the FMR in the lower metallicity part. We find that galaxies with larger E(B - V), B - R and R - H colours tend to show higher metallicity by similar to 0.05 dex at fixed stellar mass. We also find relatively clearer size dependence that objects with smaller half-light radius tend to show higher metallicity by similar to 0.1 dex at fixed stellar mass, especially in the low-mass part.