An investigation was conducted to understand the role of microstructure on the asymmetry of mechanical properties in quasi-static tension and compression in a two-phase titanium alloy Ti-5Al-3Mo-1.5V. Different microstructures were obtained (lamellar colony, basketweave and martensitic)on adopting different cooling rates after solution treatment in single phase β region. The microstructure with martensite exhibited higher strain to failure and lower yield strength than basketweave. Detailed TEM microstructural analysis helped reveal the existence of compression twins and strain-induced phase transformation in compression and tension tests respectively, both of which are relatively rare to be observed in two-phase titanium alloys. © 2019 Elsevier Ltd