We propose a novel feature fusion based multi-task convolutional neural network (ConvNet) for simultaneous bit-rate and modulation format identification (BR-MFI) and optical performance monitoring (OPM) in heterogeneous fiber-optic networks. The proposed multi-task ConvNet fuses the intermediate layers through the convolutional operation and then trains multi-task losses on the fused feature. In addition to traditional multi-task ConvNet’s ability of the feature extraction and sharing, our multi-task ConvNet is able to capture both global and local information of phase portraits and has good performance on OPM and BR-MFI tasks in a short processing time (~51 ms). The simulation results of six signals (consisted of two bit-rates and three modulation formats) demonstrate the root-mean-square (RMS) errors of the optical signal-to-noise ratio (OSNR), chromatic dispersion (CD) and differential group delay (DGD) are 0.81 dB, 1.52 ps/nm and 0.32 ps, respectively. Meanwhile, the 100% classification accuracy can be obtained for BR-MFI. Besides, the effects of the fused feature shape, the location of feature extracted for fusion, the transmitter variations and fiber nonlinearity on the performance of the proposed technique are thoroughly investigated.