An intelligent constellation diagram analyzer is proposed to implement both modulation format recognition (MFR) and optical signal-to-noise rate (OSNR) estimation by using convolution neural network (CNN)-based deep learning technique. With the ability of feature extraction and self-learning, CNN can process constellation diagram in its raw data form (i.e., pixel points of an image) from the perspective of image processing, without manual intervention nor data statistics. The constellation diagram images of six widely-used modulation formats over a wide OSNR range (15~30 dB and 20~35 dB) are obtained from a constellation diagram generation module in oscilloscope. Both simulation and experiment are conducted. Compared with other 4 traditional machine learning algorithms, CNN achieves the better accuracies and is obviously superior to other methods at the cost of O(n) computation complexity and less than 0.5 s testing time. For OSNR estimation, the high accuracies are obtained at epochs of 200 (95% for 64QAM, and over 99% for other five formats); for MFR, 100% accuracies are achieved even with less training data at lower epochs. The experimental results show that the OSNR estimation errors for all the signals are less than 0.7 dB. Additionally, the effects of multiple factors on CNN performance are comprehensively investigated, including the training data size, image resolution, and network structure. The proposed technique has the potential to be embedded in the test instrument to perform intelligent signal analysis or applied for optical performance monitoring.