The structural, electronic, and magnetic properties in (001) and (110) surfaces of quaternary Heusler alloy TiZrCoAl were investigated by spin-polarized first-principles calculations by using the Vienna ab-initio simulation package (VASP) based on density function theory. The bulk TiZrCoAl quaternary Heusler alloy was half-metallic (HM) not only using generalized gradient approximation (GGA) method but also using Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) method. For bulk TiZrCoAl alloy, there was an indirect spin-down band gap of 1.095 eV using the GGA method but there was a direct spin-down band gap of 0.460 eV at Gamma point using the HSE06 method. The HM feature was ruined in all the surfaces. The spin polarizations P were 91.6%, 97.9%, and 96.1% for TiCo termination of (001) surface, ZrAl termination of (001) surface, and TiZrCoAl termination of (110) surface, respectively, which indicated they were near HM, hence the TiZrCoAl quaternary Heusler alloy was ideal material which could be used for spintronic devices. The total magnetic moment of bulk quaternary Heusler alloy TiZrCoAl was 2.000 mu(B) per formula unit which satisfied the Slater-Pauling rule.