The present study reports nonlinear optical properties such as the first and second hyper polarizabilities (β and γ) of Y-shaped polymer (P1) and substituted polymers. The basic Y-shaped polymer (R = R1 = H) was named as P1. Upon substitution of one OCH3 group in ortho position of oxygen, it becomes polymer P2 (R1 = H, R = OCH3) and other OCH3 group on another ortho becomes P3 (R1 = R = OCH3). We have also reported structural parameters, vibrational and electronic absorption spectra of polymer, and its substituted polymers. The geometrical parameters such as dipole moment, bond length, and angles are reported at B3LYP/6-311++g** level of theory. In addition, the vibrational, electronic absorption spectra and nonlinear optical (NLO) properties are also reported at the same level of theory. There is a significant change in dipole moment and in energy observed whereas symmetry, bond length, and angles are resembling Y-shaped and substituted polymer. The vibrational spectra of Y-shaped polymer (P1) having the intense peak are C-H stretching mode observed at 1258cm-1. These theoretical vibrational modes are well matching with available experimental determinations. The method dependent hyperpolarizabilities calculated by applying the field along the X, Y, and Z direction. This study confirms the polymer P1 and P2 showing first and second hyperpolarizability response whereas P3 do not show. The electronic absorption spectra for polymer and substituted polymers are also reported at the same level of theory using (TDDFT) approach. The wavelength of electronic transition, oscillator strength, and HOMO-LUMO gap was also reported.