The effect of traffic on the content of lead and cadmium in grass morphological parts—leaves, shoots, and inflorescences—was studied. The samples were taken on a part of the European route E30 (Siedlce by road). The following plants were tested: Dactylis glomerata, Arrhenatherum elatius, and Alopecurus pratensis. During the flowering of grasses, the plant material was collected at distances of 1, 5, 10, and 15 m from the edge of the road, on the strip of road with a length of 9 km. In the collected plant parts, the content of lead and cadmium using the atomic absorption spectroscopy (AAS) method was determined. The effect of distance from the road on the content of lead and cadmium was evaluated using regression equations. Average lead content in the above parts of tested grass species was 3.56, while cadmium 0.307 mg kg−1 dry matter (DM). Lead content in plants of Alopecurus pratensis (average 4.11 mg kg−1 DM) was significantly higher than in other grasses. The lowest cadmium content, significantly different from the other species, was found in plants of Arrhenatherum elatius (0.251 mg kg−1 DM). Distance of sampling sites from the roadway significantly affects the differences in the content of cadmium and lead in plants. Analyzed aboveground plant organs of studied grasses were significantly different in contents of lead and cadmium. There were species differences in the proportions of cadmium concentration in various organs of plants. The obtained results indicate the possibility of species composition selection of grassland sward in areas with a higher risk of heavy metals associated with dust sedimentation.