In this work, we systematically study the mass spectra and strong decays of 1P and 2S charmed and charmed-strange baryons in the framework of non-relativistic constituent quark models. With the light quark cluster–heavy quark picture, the masses are simply calculated by a potential model. The strong decays are studied by the Eichten–Hill–Quigg decay formula. Masses and decay properties of the well-established 1S and 1P states can be reproduced by our method. Sigma _c(2800)^{0,+,++} can be assigned as a Sigma _{c2}(3/2^-) or Sigma _{c2}(5/2^-) state. We prefer to interpret the signal Sigma _c(2850)^0 as a 2S(1/2^+) state although at present we cannot thoroughly exclude the possibility that this is the same state as Sigma _c(2800)^0. Lambda _c(2765)^+ or Sigma _c(2765)^+ could be explained as the Lambda _c^+(2S) state or Sigma ^+_{c1}(1/2^-) state, respectively. We propose to measure the branching ratio of mathcal {B}(Sigma _c(2455)pi )/mathcal {B}(Sigma _c(2520)pi ) in the future, which may disentangle the puzzle of this state. Our results support Xi _c(2980)^{0,+} as the first radial excited state of Xi _c(2470)^{0,+} with J^P=1/2^+. The assignment of Xi _c(2930)^0 is analogous to Sigma _c(2800)^{0,+,++}, i.e., a Xi ^prime _{c2}(3/2^-) or Xi ^prime _{c2}(5/2^-) state. In addition, we predict some typical ratios among partial decay widths, which are valuable for experimental search for these missing charmed and charmed-strange baryons.