Climatological intraseasonal oscillation (CISO), as phase-locking of transient intraseasonal oscillation (ISO) to the annual cycle, is an important seasonal evolution of the Asian summer monsoon (ASM). We identified six CISO centers related to the ASM onset: the wet CISO begins from the central-to-eastern equatorial Indian Ocean (CIO) around pentad 25, which propagates eastward to the western Pacific (WP) around pentad 26, northward to the Bay of Bengal (BoB) around pentad 28, northeastward to the South China Sea (SCS) around pentad 29, and then northward to East Asia (EA) around pentad 34, while the wet CISO over the Indian summer monsoon (ISM) region peaking around pentad 32 originates from the northwestern Indian Ocean. The CISO over the CIO at pentad 25 is related to the phase-locking of Madden-Julian Oscillation (MJO), caused by the seasonal jump of the Intertropical Convergence Zone (ITCZ) from the Southern Hemisphere to the Northern Hemisphere over the Indian Ocean, signaling the beginning of the ASM CISO. The multi-model ensemble mean (MME) of the Coupled Model Intercomparison Project Phase 6 (CMIP6) models can well reproduce these strong CISOs over the ISM, BoB, SCS, and EA regions, although the simulated intensity is weaker and the peak wet phase is 2–3 pentads later than that in the observation. The very weak CISOs over the CIO and WP in the simulations challenge our subseasonal prediction of the ASM since its intraseasonal variability is usually forced by the tropical ISO. These CISOs would be significantly enhanced over the BoB and EA under the future global warming in a high emission scenario of the CMIP6 models, while the CISOs over the CIO and WP would be still absent.