In the field of biomagnetic measurements, one of the most important recent challenges is to perform measurements in a magnetically unshielded environment. This first requires that atomic magnetometers can operate in a finite magnetic field, and have enough high sensitivity. To meet these requirements, we develop a light-narrowed parametric resonance (LPR) magnetometer. By adding a modulation magnetic field to the large longitudinal magnetic field, our LPR magnetometer can measure small transverse magnetic fields with an intrinsic sensitivity of 3.5 fT/Hz1/2 in a longitudinal magnetic field of μT range. Moreover, we have also demonstrated that in contrast to the previous light-narrowed scalar magnetometers, our LPR magnetometer has the potential to achieve higher sensitivity. Because in our case spin-exchange relaxation suppression by using light narrowing can lead to an improvement of fundamental sensitivity limit regardless of which quantum noise is dominant, and hence the fundamental sensitivity is no longer limited by spin-exchange, and approaches the fundamental limit set by the spin-exchange and spin-destruction cross sections.