From November 2013 to December 2016, ambient fine particulate matter ($PM_{2.5}$) was sampled in the downtown area of Jeju City, South Korea, which has seen rapid urbanization. The atmospheric concentrations of elements were measured in the $PM_{2.5}$ samples. This study focused on Cd, Cr, Cu, Mn, Ni, Pb, As, Sb, Sn, V, and Zn. The concentrations of Al, Na, K, Fe, Ca, Mg, Sr, and La were also obtained for reference. The objectives of this study were to examine the contributions of these elements to $PM_{2.5}$ concentrations in downtown Jeju City, and to investigate the inter-element relationships and the elemental sources by using enrichment factors and principal components analysis (PCA). A composition analysis showed that the 19 elements constituted 6.65 % of the $PM_{2.5}$ mass, and Na, K, Al, Fe, Ca, Mg, and Zn constituted 98 % of the total ion mass. Seasonal trend analysis for the sampling period indicated that the concentrations of the elements increased from November to April. However, no substantial seasonal variations were found in the concentrations of the elements. The composition ratios of some elements (Cu/Zn, Cu/Cd, Cu/Pb, V/Ni, and V/La) were found to be out of range when compared to the literature from other urban areas. The ratios between the elements and the PCA results showed that local contaminant sources in Jeju City rarely influence the composition of $PM_{2.5}$. This suggests that the major sources of $PM_{2.5}$ in Jeju City may include long-range transport of fine particulate matter produced in other areas.