This work concerns divergence-free wavelet based methods for the numerical resolution of Navier-Stokes equations. It generalizes to higher dimension the approach of [23] that reformulates the projection method using the Helmholtz-Hodge decomposition in wavelet domain. The solution is searched in a finite dimensional free-slip divergence-free wavelet space, with time-dependent wavelet coefficients. We prove and verify the convergence of a first-order time numerical scheme for the Helmholtz-Hodge based projection method. Numerical simulations on the 3D Lid driven cavity flow show the accuracy and efficiency of the method.