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In this paper, we find exact string cosmological solutions for FRW cosmology,by using Hojman symmetry approach. The string cosmology under considerationincludes a scalar field $\psi(t)$ with the potential $W(\psi)$, and a totallyantisymmetric field strength $H_{\mu\nu\rho}$ which is specifically defined interms of the scale factor $a(t)$. We show that for this string cosmology,Hojman conserved quantities exist using which new exact solutions for the scalefactor and the scalar field are obtained for specific potentials $W(\psi)$ withsome free parameters. The presence of these parameters, together with those ofarising from Hojman symmetry, is an important advantage using which one canconstruct the solutions $a(t)$ and $\psi(t)$ with variety of cosmologicalbehaviors.

FRW string cosmological solutions via Hojman symmetry