Dirac states hosted by Sb/Bi square nets are known to exist in the layered antiferromagnetic ${\mathrm{AMnX}}_{2}$ (A = CaSr/Ba/Eu/Yb, X=Sb/Bi) material family with the space group to be $P4/nmm$ or $I4/mmm$. In this paper, we present a comprehensive study of quantum transport behaviors, angle-resolved photoemission spectroscopy (ARPES), and first-principles calculations on ${\mathrm{SrZnSb}}_{2}$, a nonmagnetic analog to ${\mathrm{AMnX}}_{2}$, which crystalizes in the $pnma$ space group with distorted square nets. From the quantum oscillation measurements up to 35 T, three major frequencies including ${F}_{1}=103\phantom{\rule{0.16em}{0ex}}\mathrm{T}, {F}_{2}=127\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, and ${F}_{3}=160\phantom{\rule{0.16em}{0ex}}\mathrm{T}$ are identified. The effective masses of the quasiparticles associated with these frequencies are extracted, namely, ${m}_{1}^{*}=0.1 {\mathrm{m}}_{e}, {m}_{2}^{*}=0.1 {\mathrm{m}}_{e}$, and ${m}_{3}^{*}=0.09 {\mathrm{m}}_{e}$, where ${\mathrm{m}}_{e}$ is the free electron mass. From the three band Lifshitz-Kosevich fit, the Berry phases accumulated along the cyclotron orbit of the quasiparticles are $0.06\ensuremath{\pi}, 1.2\ensuremath{\pi}$, and $0.74\ensuremath{\pi}$ for ${F}_{1}, {F}_{2}$, and ${F}_{3}$, respectively. Combined with the ARPES data and the first-principles calculations, we reveal that ${F}_{2}$ and ${F}_{3}$ are associated with the two nontrivial Fermi pockets at the Brillouin zone edge while ${F}_{1}$ is associated with the trivial Fermi pocket at the zone center. In addition, the first-principles calculations further suggest the existence of a Dirac nodal line in the band structure of ${\mathrm{SrZnSb}}_{2}$.