We study the criticality of long-range quantum ferromagnetic Ising chain with algebraically decaying interactions 1/r α via the fidelity susceptibility based on the exact diagonalization and the density matrix renormalization group techniques. We find that critical exponents change monotonously from the mean-field universality class to the short-range Ising universality class for intermediate α, which are consistent with recent results obtained from renormalization group. In addition, we determine the critical values for 1.8 ≤ α ≤ 3 from the finite-size scaling of the fidelity susceptibility. Our work provides very nice numerical data from the fidelity susceptibility for the quantum long-range ferromagnetic Ising chain. * gysun@nuaa.edu.cn † shi@nuaa.edu.cn [1] S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999). [2] X.-L. Deng, D. Porras, and J. I. Cirac, Phys. Rev. A 72, 063407 (2005).