Change detection is one of the fundamental applications of synthetic aperture radar (SAR) images. However, speckle noise presented in SAR images has a negative effect on change detection, leading to frequent false alarms in the mapping products. In this research, a novel two-phase object-based deep learning approach is proposed for multi-temporal SAR image change detection. Compared with traditional methods, the proposed approach brings two main innovations. One is to classify all pixels into three categories rather than two categories: unchanged pixels, changed pixels caused by strong speckle (false changes), and changed pixels formed by real terrain variation (real changes). The other is to group neighbouring pixels into superpixel objects such as to exploit local spatial context. Two phases are designed in the methodology: (1) Generate objects based on the simple linear iterative clustering (SLIC) algorithm, and discriminate these objects into changed and unchanged classes using fuzzy c-means (FCM) clustering and a deep PCANet. The prediction of this Phase is the set of changed and unchanged superpixels. (2) Deep learning on the pixel sets over the changed superpixels only, obtained in the first phase, to discriminate real changes from false changes. SLIC is employed again to achieve new superpixels in the second phase. Low rank and sparse decomposition are applied to these new superpixels to suppress speckle noise significantly. A further clustering step is applied to these new superpixels via FCM. A new PCANet is then trained to classify two kinds of changed superpixels to achieve the final change maps. Numerical experiments demonstrate that, compared with benchmark methods, the proposed approach can distinguish real changes from false changes effectively with significantly reduced false alarm rates, and achieve up to 99.71% change detection accuracy using multi-temporal SAR imagery.