Magnetic resonance fingerprinting (MRF) is a quantitative imaging technique that can simultaneously measure multiple important tissue properties of human body. Although MRF has demonstrated improved scan efficiency as compared to conventional techniques, further acceleration is still desired for translation into routine clinical practice. The purpose of this paper is to accelerate MRF acquisition by developing a new tissue quantification method for MRF that allows accurate quantification with fewer sampling data. Most of the existing approaches use the MRF signal evolution at each individual pixel to estimate tissue properties, without considering the spatial association among neighboring pixels. In this paper, we propose a spatially constrained quantification method that uses the signals at multiple neighboring pixels to better estimate tissue properties at the central pixel. Specifically, we design a unique two-step deep learning model that learns the mapping from the observed signals to the desired properties for tissue quantification, i.e.: 1) with a feature extraction module for reducing the dimension of signals by extracting a low-dimensional feature vector from the high-dimensional signal evolution and 2) a spatially constrained quantification module for exploiting the spatial information from the extracted feature maps to generate the final tissue property map. A corresponding two-step training strategy is developed for network training. The proposed method is tested on highly undersampled MRF data acquired from human brains. Experimental results demonstrate that our method can achieve accurate quantification for T1 and T2 relaxation times by using only 1/4 time points of the original sequence (i.e., four times of acceleration for MRF acquisition).