The lattice dynamic and elastic instabilities of zincblende (ZB) thallium nitride (TlN) under hydrostatic pressure are extensively studied to reveal the physically driven mechanism of phase transition from the ZB to a rocksalt structure using pseudopotential plane-wave density functional calculations within the local density approximation. Our calculated results shows that both transverse acoustic phonon mode softening behavior and elastic instability are responsible for the pressure-induced structural phase transition in ZB TlN