This work focus on the existence of normalized positive solutions to the following fractional Laplace equation (1.1) with a perturbation. For the mass-subcritical case, i.e., \(p \in (2,2+\frac{4\,s}{N})\) , we obtain a global minimizer with negative energy as \(h \in (\mathcal {H}_{1} ) \) . On the other hand, for the mass-supercritical case, i.e., \( p \in (2+\frac{4\,s}{N},2_{s}^{*})\) where \(2_{s}^{*}=\frac{2N}{N-2\,s}\) , there exists a mountain pass solution with positive energy as \(h \in (\mathcal {H}_{2} )\) .
