Contaminants in groundwater can spread downstream, causing risks to receptors along the path. The risk assessment of our current site groundwater contamination focuses mainly on human health risks. It rarely considers integrated risks of groundwater contamination, particularly neglecting risks to recepters at downstream locations. This study constructs a new index system and a tiered risk assessment approach for site groundwater contamination based on the “source-pathway-receptor” model considering risks to downstream receptors. For the construction of the index system, the source, pathway and receptor of site groundwater contamination are considered. For the risk assessment approach, a multi-tiered risk assessment are determined according to site groundwater contamination status. Based on the hypothetical case study of a chromium-contaminated site, four scenarios of groundwater contamination states are set. The spatio-temporal changes of groundwater contamination plumes are calculated by using the Wexler solute transport model, and risk assessment is carried out for different states of the groundwater contamination. The results show that in the two cases where the site groundwater contamination plumes have not reached the site boundary, the risk scores of the site groundwater are 4 and 6.2 points, respectively. The risk of the site groundwater at the two contamination states is low and medium, respectively. In the two cases where the site groundwater contamination plumes have arrived or exceeded the site boundary, the risk scores of the site groundwater are 7.0 and 8.8 points, respectively. The corresponding risk at the two contamination states is medium and high, respectively. It can be seen that this new method can comprehensively assess the potential level of harm of groundwater contamination to both human health and ecological environment, and therefore can provide technical support for the management of contaminated sites.