We present an all-fiber optical parametric chirped-pulse amplification integrated system delivering a single-mode polarized beam. The system makes use of a specifically designed solid-core photonic hybrid fiber (i.e., combining modified total internal reflection and photonic bandgap mechanisms) that ensures sufficient birefringence to maintain the signal polarization. Moreover, the fiber combines a large mode area to handle energetic pump pulses (without generating damage or unwanted nonlinear effects) and weak dispersion to generate parametric gain bands broad enough to amplify ultrashort pulses. An efficient parametric process allows for obtaining a very high gain (>45 dB) with an output pulse energy reaching µJ range at 1053 nm by using a single 5-m hybrid fiber amplifier.