The subbands of the ground state EC1, the first excited state EC2 and heavy hole state EHH1 are calculated by solving the eigenvalues of effective-mass Hamiltonian H0 which is derived from eight-band k·p theory and the calculations are performed at kx=ky=kz=0 for the three-dimensional array of InGaAs/GaAs quantum dots (QDs). With indium content in InGaAs QDs gradually increasing from 30% to 100%, the intersubband transition wavelength of EC2 to EC1 blue-shifts from 18.50 to 11.87 μm，while the transition wavelength of EC1 to EHH1 red-shifts from 1.04 to 1.73 μm. With the sizes of In0.5Ga0.5As and InAs QDs increasing from 1.0 to 5.0 nm, the intersubband transition from EC1 to EC2 transforms from bound-state-to-continuum-state to bound-state-to-bound-state, and the corresponding intersubband transition wavelengths red-shift from 8.12 μm (5.90 μm) to 53.47 μm (31.87 μm), respectively, and the transition wavelengths of EC1 to EHH1 red-shift from 1.13 μm (1.60 μm) to 1.27 μm (2.01 μm), respectively.