  The analysis of the mass spectrum and the calculation of the strong decay of
P-wave charmonium states strongly support to explain the newly observed X(3915)
and X(4350) as new members in P-wave charmonium family, i.e.,
$\chi_{c0}^\prime$ for X(3915) and $\chi_{c2}^{\prime\prime}$ for X(4350).
Under the P-wave charmonium assignment to X(3915) and X(4350), the $J^{PC}$
quantum numbers of X(3915) and X(4350) must be $0^{++}$ and $2^{++}$
respectively, which provide the important criterion to test P-wave charmonium
explanation for X(3915) and X(4350) proposed by this letter. The decay behavior
of the remaining two P-wave charmonium states with the second radial excitation
is predicted, and experimental search for them is suggested.
