The rate of star formation (SFR) is one of the important quantities that helps to study galaxies’ evolutionary path. In fact, measuring the SFR during the life of the Universe shows us how galaxies have acquired their metallicity and star mass. In this regard, the galaxies of the Local Group give us a great opportunity to study the connection between different stellar populations and galaxy evolution. In this paper, we use the Long-Period variable stars to estimate the radial star formation in the disc of the M31 galaxy. These stars are powerful instruments to achieve this goal. They reach their peak luminosity and coldest state at the final point of their evolution. Also, there is a directly related between their mass and luminosity, so using stellar evolution theoretical models, we construct the mass function and hence the star formation history (SFH). In the disc of M31, we see an increase in the rate of star formation and a decrease in the age of stars in the outer parts. These results predict the inside-out growth well.