In this paper, we are introducing total edge Fibonacci-like sequence irregular labeling. A total edge Fibonacci-like sequence irregular labeling f : V (G) S E(G) → {1, 2, . . . ,K} of a graph G = (V,E) is a labeling of vertices and edges of G in such a way that for any different edges xy and x 0 y 0 their weights f( x ) + f( xy ) + f( y ) and f( x 0 )+f( x 0 y 0 )+f( y 0 ) are distinct Fibonacci-like sequence numbers. The total edge Fibonacci-like sequence irregularity strength, tefls(G) is defined as the minimum K for which G has a total edge Fibonacci-like sequence irregular labeling. If a graph has a total edge Fibonacci-like sequence irregular labeling, then it is called a total edge Fibonaccilike sequence irregular graph. In this paper, we proved some standard graphs such as Pn and Cn and Book (with 3 and 4 sides) are total edge Fibonacci-like sequence irregular graphs.