This paper proposes two max-pooling engines, named the RTB-MAXP engine and the CMB-MAXP engine, with a scalable window size parameter for FPGA-based convolutional neural network (CNN) implementation. The max-pooling operation for the CNN can be decomposed into two stages, i.e., a horizontal axis max-pooling operation and a vertical axis max-pooling operation. These two one-dimensional max-pooling operations are performed by tracking the rank of the values within the window in the RTB-MAXP engine and cascading the maximum operations of the values in CMB-MAXP engine. Both the RBM-MAXP engine and the CMB-MAXP engine were implemented using VHSIC Hardware Description Language (VHDL) and verified by simulations. They have been employed for and tested in our CNN accelerator targeting at the CNN model YOLOv4-CSP-S-Leaky for object detection.