Accurate segmentation of cardiovascular structures plays an important role in many clinical applications. Recently, fully convolutional networks (FCNs), led by the UNet architecture, have significantly improved the accuracy and speed of semantic segmentation tasks, greatly improving medical segmentation and analysis tasks. The UNet architecture makes heavy use of contextual information. However, useful channel features are not fully exploited. In this work, we present an improved UNet architecture that exploits residual learning, squeeze and excitation operations, Atrous Spatial Pyramid Pooling (ASPP), and the attention mechanism for accurate and effective segmentation of complex cardiovascular structures and name it AB-ResUNet+. The channel attention block is inserted into the skip connection to optimize the coding ability of each layer. The ASPP block is located at the bottom of the network and acts as a bridge between the encoder and decoder. This increases the field of view of the filters and allows them to include a wider context. The proposed AB-ResUNet+ is evaluated on eleven datasets of different cardiovascular structures, including coronary sinus (CS), descending aorta (DA), inferior vena cava (IVC), left atrial appendage (LAA), left atrial wall (LAW), papillary muscle (PM), posterior mitral leaflet (PML), proximal ascending aorta (PAA), pulmonary aorta (PA), right ventricular wall (RVW), and superior vena cava (SVC). Our experimental evaluations show that the proposed AB-ResUNet+ significantly outperforms the UNet, ResUNet, and ResUNet++ architecture by achieving higher values in terms of Dice coefficient and mIoU.