Tropical-depression (TD)-type waves are synoptic-scale disturbances embedded with deep convection over the western North Pacific. Studies of these disturbances began over six decades ago; however, some properties of these disturbances remain vague, e.g., the coupling mechanism between the deep convection and the waves. This two-part study aims to examine the rainfall progression in TD-type disturbances and associated tropospheric moisture controlling convective rainfall. Part I investigates the rainfall and moisture characteristics of TD-type waves using TRMM-derived rainfall products and the ERA-Interim reanalysis data during the period of June-October 1998-2013. The rainfall features a north-south asymmetrical pattern with respect to a TD-type disturbance, with enhanced convective and stratiform rainfall occurring in the southern portion. Along with the northwestward propagation, deep convective and stratiform rainfall occur in-phase with the TD-type disturbance without significant preceding shallow convective rainfall. Following the deepest convection, shallow convective rainfall increases in the anomalous southerlies. Such a rainfall progression differs from the paradigm from shallow to deep convection, then to stratiform rainfall, which is suggested in other convectively coupled equatorial waves. The rainfall progression and the atmospheric moisture anomaly are phase-locked to the TD-type disturbances such that the relative displacements change little when the disturbances propagate northwestward. The latent heat release in deep convection, which is obtained from the TRMM-3G25 dataset, superposes with a broad warm anomaly in the mid-upper troposphere, suggesting wave growth through the generation of available potential energy from diabatic heating.