Let µ be a positive Borel measure on the interval [0 ,1) and µ n denote the n-th moment of the measure µ, that is, µ n = ∫ [ 0 , 1 ) t n d µ ( t ) . For 0 ∞, the generalized Ces a ̀ ro-type operator C µ , γ is defined by C µ , γ ( f ) ( z ) = ∑ n = 0 ∞ ( µ n ∑ k = 0 n Γ ( n − k + γ ) Γ ( γ )( n − k )! a k ) z n , z ∈ D where f ( z ) = ∑ n = 0 ∞ a n z n is an analytic function in D. This article is devote to study the measures µ for which C µ , γ is a bounded (resp., compact) operator from the Bloch type space B α ( 0 < α < ∞ ) into B β .