The charge-exchange spin-dipole (SD) and spin-quadrupole (SQ) strength functions of 90Zr are calculated with and without the tensor terms of the Skyrme interaction in self-consistent HF+RPA approach. It is found that, in SD and SQ transitions, the RPA correlations associated with the tensor terms shin dramatically the strengths of (Ylσ)λ = l?1 and (Ylσ)λ = 1 modes upward and downward, respectively, and also shift the strengths of (Ylσ)λ = l + 1 modes upward. The coupling between (Yl = λ ? 1σ)λ and (Yl = λ + 1σ)λ modes arising from the tensor correlation is noticeable. The RPA tensor correlations produce strengths of SD and SQ modes, which are distributed in a much wider energy range, and the (Ylσ)λ = l ? 1 modes dominate the high energy part of the strength functions. These energy shifts and coupling effects of different modes can be understood qualitatively by expressing a finite range tensor force in a separable form.