First-principles calculations based on density functional theory (DFT) are used to investigate the electronic structures and topological phase transition of arsenene under tensile and compressive strains. Buckling in arsenene strongly depends on compressive/tensile strain. The phonons band structures reveal that arsenene is dynamically stable up to 18% tensile strain and the frequency gap between the optical and acoustic branches decreases with strain. The electronic band structures show the direct bandgap decreases with tensile strain and then closes at 13% strain followed by band inversion. With spin-orbit coupling (SOC), the 14% strain-assisted topological insulator phase of arsenene is mainly governed by the p-orbitals. The SOC calculated bandgap is about 43 meV. No imaginary frequency in the phonons is observed in the topological phase of arsenene. The dynamically stable topological phase is accessed through Z2 topological invariant ν using the analysis of the parity of the wave functions at the time-reversal invariant momentum points. The calculated ν is shown to be 1, implying that arsenene is a topological insulator which can be a candidate material for nanoelectronic devices.