Using variational and numerical solutions of the mean field Gross-Pitaevskii equation, we investigate the stabilities of nonrotating and vortex solitons in Bessel optical lattice by spatial modulation of the nonlinearity(nonlinear optical lattice). It is demonstrated that there exist the stable matter-wave solitons in a combination of optical lattices with linear Bessel optical lattices and nonlinear optical lattice. Using the time-dependent variational approach, we derive the odinary differential equations for the time evolutions of the width and phase of solitons. Through an effective potential, we obtain the stable criteria for all kinds of combinations of the system parameters. We perform direct numerical simulations to support our analytical results, and find that they are in goog agreement.