The unpolarized semi-inclusive deep-inelastic scattering (SIDIS) differential cross sections in $^3$He($e,e^{prime}pi^{pm}$)$X$ have been measured for the first time in Jefferson Lab experiment E06-010 performed with a $5.9,$GeV $e^-$ beam on a $^3$He target. The experiment focuses on the valence quark region, covering a kinematic range $0.12 < x_{bj} < 0.45$, $1 < Q^2 < 4 , textrm{(GeV/c)}^2$, $0.45 < z_{h} < 0.65$, and $0.05 < P_t < 0.55 , textrm{GeV/c}$. The extracted SIDIS differential cross sections of $pi^{pm}$ production are compared with existing phenomenological models while the $^3$He nucleus approximated as two protons and one neutron in a plane wave picture, in multi-dimensional bins. Within the experimental uncertainties, the azimuthal modulations of the cross sections are found to be consistent with zero.