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The graphs used in this paper are simple, connected and finite graph. A graceful m -coloring of a graph G is a proper vertex coloring c : V (G) → { 1 , 2 , m } , where m ≥ 2 which induces a proper edge coloring c ′ : E (G) → { 1 , 2 , m − 1 } that defined by c ′ (u v) = | c (u) − c (v) |. Proper vertex coloring c of a graph G is a graceful coloring if c is a graceful m-coloring for m ∈ N. The minimum vertex coloring, that can apply such that a graph G can be colored with graceful coloring, is called a graceful chromatic number and it is denoted by χ g (G). In this paper, we will investigate the graceful chromatic number of generalized Petersen graph P (n , k) for k = 1 , 2 , 3 , 4. [ABSTRACT FROM AUTHOR]