Health indicator prediction, such as remaining useful life prediction and product quality prediction, is an important aspect of industrial intelligence. It is essential to process the massive multichannel industrial time series collected from the Industrial Internet of Things for the industrial health indicator prediction. At present, there are still three issues that need to be considered for industrial health indicator prediction. First, it is difficult to directly connect the distant positions in the industrial time series to extract the temporal relations, which decreases the efficiency of extracting the potential long-distance temporal relations and training networks. Second, it should be fully considered that data from different channels have different contributions. Equally dealing with the contributions of each channel will weaken the representational ability of prediction networks. Third, the loss function deals with early predictions and delay predictions equally, which will lead to high risks caused by delay predictions. In this article, for these issues, a novel multichannel temporal attention-based network (MCTAN) is proposed for industrial health indicator prediction, which can weigh contributions of different channels through the channel attention while avoiding the loss of the temporal information and directly connect each time series position to the local fields of the sequence through the multi-head local attention mechanism to efficiently extract potential long-distance temporal relations. Then, a weighted mean square error loss function differently dealing with early predictions and delay predictions by setting dynamic weights is presented to reduce delay predictions. Next, to deal with the above-mentioned issues systematically, a framework combining data preprocessing and MCTAN collaboratively is introduced to predict industrial health indicators through multichannel time series. Finally, the experiments are carried out on the commercial modular aero-propulsion system simulation dataset to measure the performances, including the accuracy of industrial health indicator predictions and the inference speed.