  The gross structure of compact stars composed of pion superfluid quark matter
is investigated in the frame of Nambu-Jona-Lasinio model. Under the
Pauli-Villars regularization scheme, the uncertainty of the thermodynamic
functions for inhomogeneous states is cured, and the LOFF state appeared in the
hard cutoff scheme is removed from the phase diagram of pion superfluid.
Different from the unpaired quark matter and color superconductor, the strongly
coupled pion superfluid in the state close to the BCS limit is a possible
candidate of compact stars with mass $M\simeq 3M_{\odot }$ and radius $R\simeq
14$ km.
