  A new detection method for gravitational waves (GWs) with ultra-low
frequencies ($f_{\rm GW} \lesssim 10^{-10}~{\rm Hz}$), which is much lower than
the range of pulsar timing arrays (PTAs), was proposed in Yonemaru et al.
(2016). This method utilizes the statistical properties of spin-down rates of
milli-second pulsars (MSPs) and the sensitivity was evaluated in Yonemaru et
al. (2018). There, some simplifying assumptions, such as neglect of the "pulsar
term" and spatially uniform distribution of MSPs, were adopted and the
sensitivity on the time derivative of GW amplitude was estimated to be
$10^{-19}~{\rm s}^{-1}$ independent of the direction, polarization and
frequency of GWs. In this paper, extending the previous analysis, realistic
simulations are performed to evaluate the sensitivity more reasonably. We adopt
a model of 3-dimensional pulsar distribution in our Galaxy and take the pulsar
term into account. As a result, we obtain expected sensitivity as a function of
the direction, polarization and frequency of GWs. The dependence on GW
frequency is particularly significant and the sensitivity becomes worse by a
few orders for $< 10^{-12}~{\rm Hz}$ compared to the previous estimates.
