  Aims: We provide a new distance estimate for the Pleiades based on the moving
cluster method, which will be useful to further discuss the so-called Pleiades
distance controversy and compare it with the very precise parallaxes from the
Gaia space mission.
  Methods: We apply a refurbished implementation of the convergent point search
method to an updated census of Pleiades stars to calculate the convergent point
position of the cluster from stellar proper motions. Then, we derive individual
parallaxes for 64 cluster members using radial velocities compiled from the
literature, and approximate parallaxes for another 1146 stars based on the
spatial velocity of the cluster. This represents the largest sample of Pleiades
stars with individual distances to date.
  Results: The parallaxes derived in this work are in good agreement with
previous results obtained in different studies (excluding Hipparcos) for
individual stars in the cluster. We report a mean parallax of $7.44\pm
0.08$~mas and distance of $134.4^{+2.9}_{-2.8}$pc that is consistent with the
weighted mean of $135.0\pm 0.6$pc obtained from the non-Hipparcos results in
the literature.
  Conclusions: Our result for the distance to the Pleiades open cluster is not
consistent with the Hipparcos catalog, but favors the recent and more precise
distance determination of $136.2\pm 1.2$pc obtained from Very Long Baseline
Interferometry observations. It is also in good agreement with the mean
distance of $133\pm 5$pc obtained from the first trigonometric parallaxes
delivered by the Gaia satellite for the brightest cluster members in common
with our sample.
