In this paper, we present a fast algorithm for solving the space-fractional Gross-Pitaevskii equation while preserving the law of mass conservation. First we discretize this equation by using a second-order weighted and shifted Grünward difference operator and obtain a system of semilinear differential equations with linear and nonlinear parts. Afterwards, we employ a Strang splitting method to solve this semi-discretization scheme. To further reduce computational time, we propose a two-level Strang splitting method from the linear part. This method significantly reduces computational complexity to O(nlog⁡n) by implementing the fast Fourier transform. Importantly, our proposed method ensures the unconditional preservation of mass conservation and achieves second-order convergence. At last, we demonstrate the validity of our approach through numerical experiments and graphical results presented.