  Relativistic electrons accelerated by both the first-order and the
second-order Fermi accelerations in some synchrotron sources have a hybrid
shape of thermal and nonthermal energy distribution. This particle acceleration
result is supported by some recent numerical simulations. We calculate the
synchrotron polarization by applying this electron energy distribution. The
polarization degrees in the cases of active galactic nucleus (AGN) jets and
gamma-ray bursts (GRBs) are given as examples. The possible application for the
polarization study of Sgr A* is also mentioned. We finally suggest high-energy
polarization measurements for these synchrotron sources to test our results.
