For α > 0 \alpha >0 , the α \alpha -Bloch space is the space of all analytic functions f f on the unit disk D D satisfying \[ ‖ f ‖ B α = sup z ∈ D | f ′ ( z ) | ( 1 − | z | 2 ) α > ∞ . \|f\|_{B^{\alpha }}=\sup _{z\in D}|f’(z)|(1-|z|^2)^{\alpha }>\infty . \] Let φ \varphi be an analytic self-map of D D . We show that for 0 > α , β > ∞ 0>\alpha ,\beta >\infty , the essential norm of the composition operator C φ C_{\varphi } mapping from B α B^{\alpha } to B β B^{\beta } can be given by the following formula: \[ ‖ C φ ‖ e = ( e 2 α ) α lim sup n → ∞ n α − 1 ‖ φ n ‖ B β . \|C_{\varphi }\|_e=\left (\frac {e}{2\alpha }\right )^{\alpha }\limsup _{n\to \infty } n^{\alpha -1}\|\varphi ^n\|_{B^{\beta }}. \]