Clinically, knowing the number of red blood cells (RBCs) and white blood cells (WBCs) helps doctors to make the better decision on accurate diagnosis of numerous diseases. The manual cell counting is a very time-consuming and expensive process, and it depends on the experience of specialists. Therefore, a completely automatic method supporting cell counting is a viable solution for clinical laboratories. This paper proposes a novel blood cell counting procedure to address this challenge. The proposed method adopts SegNet - a deep learning semantic segmentation to simultaneously segment RBCs and WBCs. The global accuracy of the segmentation of WBCs, RBCs, and the background of peripheral blood smear images obtains 89% when segment WBCs and RBCs from the background of blood smear images. Moreover, an effective solution to separate grouped or overlapping cells and cell count is presented using Euclidean distance transform, local maxima, and connected component labeling. The counting result of the proposed procedure achieves an accuracy of 93.3% for red blood cell count using dataset 1 and 97.38% for white blood cell count using dataset 2.