The two well-known numerical radius inequalities for the tensor product A⊗ B acting on H⊗ K, where A and B are bounded linear operators defined on complex Hilbert spaces H and K, respectively are 12‖A‖‖B‖≤w(A⊗B)≤‖A‖‖B‖ and w(A) w(B) ≤ w(A⊗ B) ≤ min { w(A) ‖ B‖ , w(B) ‖ A‖ }. In this article, we develop new lower and upper bounds for the numerical radius w(A⊗ B) of the tensor product A⊗ B and study the equality conditions for those bounds.