In this work, we systematically study the mass spectra and strong decays of 1 P and 2 S 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 1 S and 1 P states can be reproduced by our method. Σ c ( 2800 ) 0 , + , + + can be assigned as a Σ c 2 ( 3 / 2 - ) or Σ c 2 ( 5 / 2 - ) state. We prefer to interpret the signal Σ c ( 2850 ) 0 as a 2 S ( 1 / 2 + ) state although at present we cannot thoroughly exclude the possibility that this is the same state as Σ c ( 2800 ) 0 . Λ c ( 2765 ) + or Σ c ( 2765 ) + could be explained as the Λ c + ( 2 S ) state or Σ c 1 + ( 1 / 2 - ) state, respectively. We propose to measure the branching ratio of B ( Σ c ( 2455 ) π ) / B ( Σ c ( 2520 ) π ) in the future, which may disentangle the puzzle of this state. Our results support Ξ c ( 2980 ) 0 , + as the first radial excited state of Ξ c ( 2470 ) 0 , + with J P = 1 / 2 + . The assignment of Ξ c ( 2930 ) 0 is analogous to Σ c ( 2800 ) 0 , + , + + , i.e., a Ξ c 2 ′ ( 3 / 2 - ) or Ξ c 2 ′ ( 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.