The author studies a particular case of Finsler metrics, so-called \((\alpha, \beta)\)-metrics (i.e. of the form \(F=\alpha\phi(\beta/\alpha)\) where \(\alpha\) is a Riemann metric and \(\beta\) is a 1-form). It is proven that such a metric – under some conditions – is projectively flat (namely, geodesics are straight lines) on an open set if and only if \(\phi\), \(\beta\) and \(\alpha\) satisfy some conditions described nicely in the paper. This result generalizes the case where \(\phi(s)=1+s\) (i.e. a Randers metric) (see, e.g., [S. -S. Chern and Z. Shen , Riemann-Finsler geometry. Nankai Tracts in Mathematics 6. (Hackensack), NJ: World Scientific. (2005; Zbl 1085.53066)]).