In this paper we gave an estimate of the order of the best approximation byrational functions with fixed poles in Hp'Hw class. The main result of this paper is the following theorem: For any function f(z)∈Hp'Hw(|z|<1)

P≥1

there is the estimate ρ(f

Z)≤A·integral from n=0 to 1/ (w(t)/tdt+ce)~((-1/10)) in which the constant A doesn't depend on A and f

the constant c doesn't depend on

and =sum from k=1 to n (1-1/|zk|)

where Z={zk}k-1n is a finite or infinite sequence of (possibly repeated) points in the extended complex plane.