We give some conditions for the self-adjoint operators associated with the $q$-Sturm--Liouville expression \[ au y:=-\frac1q D_{q^{-1}}(p(x)D_qy(x))+r(x),\;\;-ıfty<x<ıfty. \] to have a discrete spectrum, and investigate the continuous spectra of these operators. We also prove that the regular symmetric $q$-Sturm--Liouville operator is semi-bounded from below which is not studied in literature yet.