Acid mine drainage (AMD) threatens water resources. Research on the treatment effect of heavy metals in AMD using constructed wetlands has been conducted, most often indoors and in short cycles. This study considered an AMD-constructed wetland that had operated for 12 years as the research subject. Water, sediments, and wetland plant samples were analyzed from different sampling points in the wetland to study the treatment effect of constructed wetlands on AMD and to explore the distribution characteristics of heavy metals in constructed wetlands. The results indicated that the constructed wetlands achieved removal rates of 97.59% for Fe and 83.05% for Mn in AMD. At the outlet of the wetlands, Fe, Mn, Cu, and Zn all met the Class III standard of “surface water environmental quality standards” (GB3838-2002). The content of heavy metals in the sediments was as follows: Fe>Mn>Zn>Pb>Cu>Cd. The contents of heavy metals in the rhizosphere sediments were higher than those in the non-rhizosphere sediments. The maximum concentrations of Fe, Mn, Cu, Zn, Pb, and Cd were 3.44, 10.67, 3.91, 3.50, 2.52, and 12.22 times that of the control group, respectively. Plants have a strong ability to accumulate heavy metals. Except for Mn, various elements were enriched in the surface areas of plant roots. The enrichment effect of rhizosphere sediments and plant surfaces is important in removing heavy metals from AMD.