The goal of salient region detection is to identify the regions of an image that attract the most attention. Many methods have achieved state-of-the-art performance levels on this task. Recently, salient instance segmentation has become an even more challenging task than traditional salient region detection; however, few of the existing methods have concentrated on this underexplored problem. Unlike the existing methods, which usually employ object proposals to roughly count and locate object instances, our method applies salient objects subitizing to predict an accurate number of instances for salient instance segmentation. In this paper, we propose a multitask densely connected neural network (MDNN) to segment salient instances in an image. In contrast to existing approaches, our framework is proposal-free and category-independent. The MDNN contains two parallel branches: the first is a densely connected subitizing network (DSN) used for subitizing prediction; the second is a densely connected fully convolutional network (DFCN) used for salient region detection. The MDNN simultaneously outputs saliency maps and salient object subitizing. Then, an adaptive deep feature-based spectral clustering operation segments the salient regions into instances based on the subitizing and saliency maps. The experimental results on both salient region detection and salient instance segmentation datasets demonstrate the satisfactory performance of our framework. Notably, its APr@0.5 and Apr@0.7 reaches 73.46% and 60.14% in the salient instance dataset, substantially higher than the results achieved by the state-of-the-art algorithm.