First-principles calculations are performed to investigate the ferroelectric and dielectric properties of (001) epitaxial SrZrO3 thin films under misfit strain. A rich phase diagram is predicted. By condensing the polar instability, the ferroelectric Pmc21 and Ima2 phases can coexist under tensile strain (about 3.7%-5.2%/5.7%). Combining in-plane ferroelectric (FExy) and out-of-plane in-phase antiferrodistortive (IAFDz) modes, another new Pmc21 state (P > 56 μC cm(-2)) occurs with increase in the tensile strain. The paraelectric I4/mcm and ferroelectric P4mm phases emerge around -3.2%/-3.7% and -6.4%/-7.4% compressive strain, respectively. The former exhibits an intense out-of-plane dielectric response, while the latter possesses a rather large polarization (∼ 110 μC cm(-2)). The large polarization and dielectric response are discussed in relationship to strain-driven structural distortion.