Considering the mass, parity and D 0 p decay mode, we tentatively assign the Λ c (2940) as the P−wave states with one radial excitation. Then, via studying the strong decay behavior of the Λ c (2940) within the 3 P 0 model, we obtain that the total decay widths of the Λ c1 ( 1 2 − , 2P) and Λ c1 ( 3 2 − , 2P) states are 16.27 MeV and 25.39 MeV, respectively. Compared with the experimental total width 27.7 +8.2 −6.0 ± 0.9 +5.2 −10.4 MeV measured by LHCb Collaboration, both assignments are allowed, and the J P = 3 2 − assignment is more favorable. Other λ−mode Σ c (2P) states are also investigated, which are most likely to be narrow states and have good potential to be observed in future experiments.