Eigenstates and intersubband transition energies of a T-shaped quantum wire embedded in square quantum wire are numerically computed by solving time-independent Schrödinger equation using finite difference technique. Dimensions of arm well and stem wells and material composition of shell layer is varied to observe the change in transition energies. Al x Ga 1-x As/GaAs composition is considered for simulation purpose with appropriate boundary conditions, arises due to geometrical nature and effective mass mismatch at heterojunction along with conduction band discontinuity. Transition energy is plotted for lowest three eigenstates. Results establish that T-shaped structure is one of the promising candidates for quantum wire laser.