  We show that an interesting of pairing occurs for spin-imbalanced Fermi gases
under a specific experimental condition---the spin up and spin down Fermi
levels lying within the $p_x$ and $s$ orbital bands of an optical lattice,
respectively. The pairs condense at a finite momentum equal to the sum of the
two Fermi momenta of spin up and spin down fermions and form a $p$-orbital pair
condensate. This $2k_F$ momentum dependence has been seen before in the spin-
and charge- density waves, but it differs from the usual $p$-wave superfluids
such as $^3$He, where the orbital symmetry refers to the relative motion within
each pair. Our conclusion is based on the density matrix renormalization group
analysis for the one-dimensional (1D) system and mean-field theory for the
quasi-1D system. The phase diagram of the quasi-1D system is calculated,
showing that the $p$-orbital pair condensate occurs in a wide range of
fillings. In the strongly attractive limit, the system realizes an
unconventional BEC beyond Feynman's no-node theorem. The possible experimental
signatures of this phase in molecule projection experiment are discussed.
