  The 2$\alpha+t$ cluster structure in $^{11}$B is investigated by the
microscopic generator coordinate method (GCM) with the Brink cluster wave
functions. With a proper choice of the parameters of the effective interaction,
the calculated energy spectrum shows reasonable agreement with the observed
low-lying spectra of both parities. On the basis of the calculated radii,
monopole and $B(E2)$ transition strengths, several developed cluster states of
$^{11}$B are suggested. For the negative-parity states, in addition to the
well-known $3/2_3^-$ cluster state, the $1/2_2^-$ and $5/2_3^-$ states are also
proposed as the well-developed cluster states. For the positive-parity states,
it is found that many states around the 2$\alpha+t$ threshold show the feature
of developed clusters. In particular, the $1/2_2^+$ state is found to have a
linear-chain-like structure, which is consistent with the previous
antisymmetrized molecular dynamics calculation, but contradicts to the
orthogonality condition model calculation. It is also found that many of these
positive-parity cluster candidates have the non-negligible isoscalar dipole
transition strengths, which require the experimental confirmation.
