In this article we study the Schrödinger equation associated with Harmonic oscillator in the form of Strichartz type inequality. We give simple proofs for Strichartz type inequalities using purely the \(L^2 \rightarrow L^p\) operator norm estimates of the spectral projections associated to the harmonic oscillator proved in [Jeong, Lee and Ryu, 2022 arxiv:2205.03036v1, 2022, and Koch and Tataru 2005 Duke Math. J. 128:369–392, 2005]. Our Strichartz type estimates are sharp in sense of regularity of initial data.