Aims. Our goal is to estimate the star formation main sequence (SFMS) and the star formation rate density (SFRD) at z ≤ 0.017 (d ≲ 75 Mpc) using the Javalambre Photometric Local Universe Survey (J-PLUS) first data release, that probes 897.4 deg2 with twelve optical bands. Methods. We extract the Hα emission flux of 805 local galaxies from the J-PLUS filter J0660, being the continuum level estimated with the other eleven J-PLUS bands, and the dust attenuation and nitrogen contamination corrected with empirical relations. Stellar masses (M⋆), Hα luminosities (LHα), and star formation rates (SFRs) were estimated by accounting for parameters covariances. Our sample comprises 689 blue galaxies and 67 red galaxies, classified in the (u − g) vs. (g − z) color–color diagram, plus 49 AGN. Results. The SFMS is explored at log M⋆ ≳ 8 and it is clearly defined by the blue galaxies, with the red galaxies located below them. The SFMS is described as log SFR = 0.83log M⋆ − 8.44. We find a good agreement with previous estimations of the SFMS, especially those based on integral field spectroscopy. The Hα luminosity function of the AGN-free sample is well described by a Schechter function with log LHα∗ = 41.34, log ϕ* = −2.43, and α = −1.25. Our measurements provide a lower characteristic luminosity than several previous studies in the literature. Conclusions. The derived star formation rate density at d ≲ 75 Mpc is log ρSFR = −2.10 ± 0.11, with red galaxies accounting for 15% of the SFRD. Our value is lower than previous estimations at similar redshift, and provides a local reference for evolutionary studies regarding the star formation history of the Universe.