  In this paper, we establish the global well-posedness of stochastic 3D
Leray-$\alpha$ model with general fractional dissipation driven by
multiplicative noise. This model is the stochastic 3D Navier-Stokes equation
regularized through a smoothing kernel of order $\theta_1$ in the nonlinear
term and a $\theta_2$-fractional Laplacian. In the case of $\theta_1 \ge 0,
\theta_2 > 0$ and $\theta_1+\theta_2 \geq\frac{5}{4}$, we prove the global
existence and uniqueness of strong solutions. The main results cover many
existing works in the deterministic cases, and also generalize some known
results of stochastic models as our special cases such as stochastic
hyperviscous Navier-Stokes equation and classical stochastic 3D Leray-$\alpha$
model.
