  The non-Markovianity is a prominent concept of the dynamics of the open
quantum systems, which is of fundamental importance in quantum mechanics and
quantum information. Despite of lots of efforts, the experimentally measuring
of non-Markovianity of an open system is still limited to very small systems.
Presently, it is still impossible to experimentally quantify the
non-Markovianity of high dimension systems with the widely used
Breuer-Laine-Piilo (BLP) trace distance measure. In this paper, we propose a
method, combining experimental measurements and numerical calculations, that
allow quantifying the non-Markovianity of a $N$ dimension system only scaled as
$N^2$, successfully avoid the exponential scaling with the dimension of the
open system in the current method. After the benchmark with a two-dimension
open system, we demonstrate the method in quantifying the non-Markovanity of a
high dimension open quantum random walk system.
