  We obtain the general expression of the gluon propagator at finite
temperature ($T$) and in a magnetic field ($B$), for the case that the four
transverse tensor structures appear in the gluon self-energy. By using this
expression and a specific form of the one-loop gluon self-energy in the lowest
Landau level approximation, we analyze the gluon spectrum in the strong
magnetic field limit. As a result, we find that there exist two collective
excitations of which the energies are of the order of $p\sim gT$ with $g$ being
the coupling constant. One of the two excitations enjoys properties quite
different from those of the collective excitations at $B=0$ which have been
discussed by using the hard thermal loop approximation. We also discuss the
static and dynamical screening effects, which are expected to be important for
computation of transport coefficients in strong magnetic fields.
