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The statistical characteristics of precipitation play an extremely important role in the risk assessment of drought and flood disasters and water resource management. In this paper, the precipitation concentration degree (PCD), precipitation concentration period (PCP) and precipitation concentration index (PCI) were used to analyse the spatiotemporal variation in precipitation concentration characteristics in China from 1960 to 2015. In addition, the cross-wavelet transform was used to analyse the possible dependencies and spatial characteristics between these three precipitation concentration indices (PCD, PCP and PCI) and monsoon indices (East Asian summer monsoon index, EASMI; South Asian summer monsoon index, SASMI; and South China Sea summer monsoon index, SCSSMI) of nine river basins in China. The results show that the spatial distribution of precipitation concentration indices in China has obvious north-south and east-west variability. China's precipitation concentration indices are generally declining, with weak volatility. Among these indices, the PCD (P < 0.05) and PCI (P < 0.01) have decreased significantly at rates of − 0.005/10 year and − 0.006/10 year, respectively, while there has been no obvious decrease in the PCP. Compared with the PCD before 1978, the PCD in the rainy season after 1978 has decreased. In most areas, the rainy season is concentrated in July every year; however, the rainy season has been delayed in the middle and lower reaches of the Yangtze River and has advanced mainly in the other basins. The PCI has declined since 1978, indicating a decreasing contribution of heavy precipitation to the total annual precipitation, but this change in the PCI has occurred mainly at high-value stations (PCI > 0.7), and the PCI at low-value stations has increased. Most of China's precipitation concentration indices and monsoon indices, as well as the NWRB, have small-scale (2–4 years) or medium-scale (12–15 years) oscillation periods. The oscillation periods between the precipitation concentration indices and monsoon indices in the Yangtze and Pearl River basins are more significant than those in other basins. The results of this study can help to understand the differences among the precipitation concentration characteristics in different basins in China and the intrinsic relationship between these characteristics and the summer monsoon and provide a reference for further research. [ABSTRACT FROM AUTHOR]