  In this paper, using blow-up analysis, we prove a quantization result for an
elliptic equation with critical exponential growth on compact Riemannian
surface without boundary. Similar results for Euclidean space were obtained by
Adimurthi-Struwe \cite{Adi-Stru}, Druet \cite{Druet}, Lamm-Robert-Struwe
\cite{L-R-S}, Martinazzi \cite{Mart}, Martinazzi-Struwe \cite{Mar-Stru}, and
Struwe \cite{Struwe} respectively.
