This manuscript reports a study of the after-pulse properties of different types of 20-inch photomultiplier tubes (PMTs), especially for the 20-inch microchannel-plate-PMTs (MCP-PMTs) for JUNO experiment. In the study, the after-pulse rate (APR) is calculated from PMT waveforms obtained by a CAEN DT5751 waveform digitizer. We tested the after-pulse characteristics of both Dynode-PMTs and MCP-PMTs and made a thorough study on the after-pulses of high quantum efficiency (HQE) MCP-PMT for JUNO experiment, including their time distribution, after-pulse rate and the causes of different after-pulse groups through flight time analysis. Based on a fast test method, individual tests on 28 HQE-MCP-PMTs on the after-pulses were conducted at the North Night Vision Tech. Ltd. (NNVT) in Nanjing in December of 2019. This paper reports the average APR under two different definitions for HQE-MCP-PMTs and the proportions of the five different after-pulse groups.