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The conformable Sturm–Liouville problem (CSLP), −x1−αpxx1−αy′x′=λρx−qxyx, for 0<α≤1, is studied under some certain conditions on the coefficients p, ρ, and q. According to an interesting idea proposed by P. Binding and H. Volkmer [Binding et al., 2012, Binding et al., 2013], we will derive how to reduce the periodic or antiperiodic (CSLP) to an analysis of the Prüfer angle. The eigenvalue interlacing property related to (CSLP) will be given.