Respiration is known to reflect our health condition, which motivates researchers to develop various radar-based respiration rate estimation methods. However, these conventional methods do not work, when a subject is not right in front of the radar. In this paper, we propose a novel CNN (Convolutional Neural Network)-based respiration rate estimation method in indoor environments via a MIMO (Multiple-Input Multiple-Output) FMCW (Frequency Modulated Continuous Wave) radar. A MIMO FMCW radar can estimate the DoA (Direction of Arrival) and the distance between a MIMO FMCW radar and an object. Thus, the respiration can be captured based on the phase variation at a subject's location. However, even when the advanced signal processing, e.g., MUSIC (MUltiple SIgnal Classification) algorithm, is used, it is difficult to estimate the DoA and the distance in indoor environments due to the large effect of multipath. To deal with this problem, in the proposed method, phase variations against various locations are calculated from the received signals of a MIMO FMCW radar, and then spectrograms are calculated from the phase variations. Each spectrogram is subsequently fed into the CNN that outputs the respiration rates, e.g., 0.1 Hz, 0.2 Hz, and non-respiration, i.e., a spectrogram without the effect of respiration, where is one of the deep learning techniques that have been successfully applied to the image recognition. Through the experiments we confirmed that except for when microwaves were not transmitted directly toward a subject's chest due to furniture, the proposed method accurately estimated the respiration rate, regardless of the situation.