Abstract: Many scholars studied the Q_K spaces and the Bloch space of holomorphic functions in the unit disk in the complex plane, where K(r) are right continuous nondecreasing functions on (0,+∞). However, it is very difficult to describe the compact Cesàro operators between these spaces. Let 0<α<+∞ and ∫¹₀(1-r²)^-1K(-logr)rdr<+∞,g is a holomorphic function in the unit disk, thus, a sufficient and necessary condition for the extended Cesàro operators T_g from Q_K spaces into α-Bloch spaces in the unit disc to be compact is obtained.

Key words: Q_K spaces, Bloch type spaces, extended Cesàro operator