Free electrons can screen out long-range Coulomb interaction and destroy the polar distortion in some ferroelectric materials, whereas the coexistence of polar distortion and metallicity were found in several non-centralsymmetric metals (NCSMs). Therefore, the mechanisms and designing of NCSMs have attracted great interests. In this work, by first-principles calculation, we found the polar distortion in the lone-pair driven ferroelectric material PbTiO3 can not only persist, but also increase with electron doping. We further analyzed the mechanisms of the persisting of the polar distortion. We found that the Ti site polar instability is suppressed but the Pb site polar instability is intact with the electron doping. The Pb-site instability is due to the lone-pair mechanism which can be viewed as a pseudo-Jahn-Teller effect, a mix of the ground state and the excited state by ion displacement from the central symmetric position. The lone-pair mechanism is not strongly affected by the electron doping because neither the ground state nor the excited state involved is at the Fermi energy. The enhancement of the polar distortion is related to the increasing of the Ti ion size by doping. These results show that the long-pair stereoactive ions can be used for designing NCSMs.Although the NCSM structures are no longer suitable for the usage as ferroelectric materials because of the metallicity, other interesting properties are found in NCSMs, like the unconventional optical responses 15,16 , magnetoelectricity 17 , superconductivity 18 , and thermoelectricity 13 . A deeper understanding of the mechanisms of NCSM could help finding new NCSMs. The purpose of this work is to seek a possible mechanism of NCSMs so new NCSMs can be found or designed.In this work, by studying the polar distortion in electrondoped PbTiO 3 , we show that the lone-pair driven polar distortion is compatible with metallicity. The lone pair mechanism for the polar distortion in non-doped PbTiO 3 has been long studied [19][20][21][22] . In PbTiO 3 , the hybridization between the Pb (6s, 6p) bands and O 2p bands reduces the short-range repulsion, resulting in a large polar distortion, which is often referred as lone-pair driven ferroelectricity. The lone-pair driven ferroelectricity can be interpreted as the result of the Pseudo-Jahn-Teller effect (PJTE). 23-26 which is local. Therefore, it is possible that the lone pair mechanism can still drive the polar distortion even if the long-range interaction is screened. We found that the polar distortion in PbTiO 3 not only persists but also is enhanced with the electron doping. Then by analyzing the evolution of the phonon and the force constant matrices (FCM's), we found that the A-site instability, which is caused by the lone-pair mechanism, is responsible for the persisting of the polar distortion, because the electronic states involved are far away from the Fermi energy. We showed that enhancement of the polar distortion is related to the increasing of the Pb-O distance. We discussed the generalizability...