The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({alpha},;{eta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.