Magnetic resonance fingerprinting (MRF) is a novel quantitative imaging technique that allows simultaneous measurements of multiple important tissue properties in human body, e.g., T1 and T2 relaxation times. While MRF has demonstrated better scan efficiency as compared to conventional quantitative imaging techniques, further acceleration is desired, especially for certain subjects such as infants and young children. However, the conventional MRF framework only uses a simple template matching algorithm to quantify tissue properties, without considering the underlying spatial association among pixels in MRF signals. In this work, we aim to accelerate MRF acquisition by developing a new post-processing method that allows accurate quantification of tissue properties with fewer sampling data. Moreover, to improve the accuracy in quantification, the MRF signals from multiple surrounding pixels are used together to better estimate tissue properties at the central target pixel, which was simply done with the signal only from the target pixel in the original template matching method. In particular, a deep learning model, i.e., U-Net, is used to learn the mapping from the MRF signal evolutions to the tissue property map. To further reduce the network size of U-Net, principal component analysis (PCA) is used to reduce the dimensionality of the input signals. Based on in vivo brain data, our method can achieve accurate quantification for both T1 and T2 by using only 25% time points, which are four times of acceleration in data acquisition compared to the original template matching method.