Magnetic Resonance (MR) Fingerprinting is an emerging transient-state imaging paradigm, which enables the quantization of multiple MR tissue parameters in a single experiment. Balanced steady-state free precession (bSSFP)-based MR Fingerprinting has excellent signal-to-noise characteristics and also allows for acquiring both tissue parameter maps and field inhomogeneity maps. However, field inhomogeneity often results in complex magnetization evolutions in bSSFP-based MR Fingerprinting, which creates significant challenges in image reconstruction. In this paper, we introduce a new method to address the image reconstruction problem. The proposed method incorporates a low-dimensional nonlinear manifold learned from an ensemble of magnetization evolutions using a deep autoencoder. It provides much better representation power than a low-dimensional linear subspace in capturing complex magnetization evolutions. We formulate the image reconstruction problem with this nonlinear model and solve the resulting optimization problem using an algorithm based on variable splitting and the alternating direction method of multipliers. We evaluate the performance of the proposed method using numerical experiments and demonstrate that it significantly outperforms the state-of-art method using a linear subspace model.