This paper proposes the design and analysis for a multivariable Newton-based stochastic extremum seeking control under delays. Multi-input systems with different time delays in each individual input channel are dealt with. A new predictor feedback with stochastic sinusoidal pertubation-based estimates of the Hessian's inverse is incorporated in closed loop such that the convergence rate of the real-time optimizer can be made user-assignable. Exponential stability and convergence to a small neighborhood of the unknown extremum point can be obtained. This result is rigorously reached by using backstepping transformation and averaging in infinite dimensions. A numerical example is shown in order to present the effectiveness of the proposed predictor-based stochastic extremum seeking for time-delay compensation.