Context. To understand the formation and evolution of galaxies, it is important to have a full comprehension of the role played by metallicity, star formation rate (SFR), morphology, and color. The interplay of these parameters at different redshifts will substantially affect the evolution of galaxies and, as a consequence, their evolution provides important clues and constraints for the galaxy evolution models. Aims: In this work we focus on the evolution of the SFR, metallicity of the gas, and morphology of galaxies at low redshift in search of signs of evolution. We analyzed the evolution of the SFR, metallicity, and morphology, through the mass-metallicity, luminosity-metallicity, SFR-stellar mass, and SFR-metallicity relationships of star-forming galaxies from SDSS-DR5 (Sloan Digital Sky Survey-Data Release 5), using redshift intervals in bins of 0.1 from ~0 to 0.4. Methods: We used data processed with the STARLIGHT spectral synthesis code, correcting the fluxes for dust extinction, and estimating metallicities using the R23 method. We used the S2N2 (log(Hα/[S ii]) vs. log(Hα/[N ii])) diagnostic diagram as a tool to classify star-forming, composite, and AGN galaxies. We analyzed the evolution of the three principal BPT diagrams, estimating the SFR and specific SFR (SSFR) for our samples of galaxies, studying the luminosity and mass-metallicity relations, and analyzing the morphology of our sample of galaxies through the g-r color, concentration index, and SSFR. Results: We found that the S2N2 is a reliable diagram for classifying star-forming, composite, and AGNs galaxies. We demonstrate that the three principal BPT diagrams show an evolution toward higher values of [O iii] λ5007/Hβ due to a metallicity decrement. We found an evolution in the mass-metallicity relation of ~0.2 dex for the redshift range 0.3 < z < 0.4 compared to our local one. From the analysis of the evolution of the SFR and SSFR as a function of the stellar mass and metallicity, we discovered a group of galaxies with higher SFR and SSFR at all redshift samples, whose morphology is consistent with those of late-type galaxies. Finally, the comparison of our local (0.04 < z < 0.1) with our higher redshift sample (0.3 < z < 0.4) shows that the metallicity, the SFR, and morphology evolve toward lower values of metallicity, higher SFRs, and late-type morphologies for the redshift range 0.3 < z < 0.4.