Balanced steady-state free precession (bSSFP) is one of the fast magnetic resonance imaging techniques which is commonly used in clinics due to its excellent signal-to-noise ratio (SNR) and short scan time. For data acquisition, a centric phase-encoding (PE) order is preferred to a linear order in order to maximize prepared magnetization contrast for physiological imaging. However, the centric PE scheme in bSSFP makes abrupt changes in the amplitude and polarity of the PE gradients, which causes irregular eddy-current dephasing, resulting in significant image artifacts. Several compensation strategies have been devised such as pairing and double averaging (dAVE), but pairing can achieve an incomplete compensation and dAVE is not suitable for physiological imaging due to its doubled scan time. In this study, we propose (i) a pseudo-centric PE-grouping (PE-grouping) which is a hybrid of the conventional centric and linear orders for optimal contrast and minimal signal fluctuations. Also, we propose (ii) four averaging strategies which further reduce the residual eddy-current and transient oscillation artifacts by averaging two full images so that oppositely-oscillating signals of two images can be canceled out. The proposed strategies markedly removed eddy-current and transient oscillation artifacts for both phantom and in vivo while maintaining the SNR and temporal resolution of the conventional centric scheme, providing results better than those of the pairing and comparable to those of dAVE. In conclusion, proposed schemes are expected to improve the image quality of physiological bSSFP imaging with less artifact and same temporal resolution of the conventional centric scheme.