  In this paper, we propose a feasible conjugate gradient (FCG) method for
calculating ${\mathcal B}$-eigenpairs of a symmetric tensor ${\mathcal A}$. The
method is an extension of the well-known conjugate gradient method for
unconstrained optimization problems to some curve constrained optimization
problems. The proposed FCG method can find a ${\mathcal B}$-eigenpair of a
symmetric tensor ${\mathcal A}$ without the requirement that the orders of
${\mathcal A}$ and $\mathcal B$ are equal. We pay particular attention to the
Polak-Rib\'ire-Polyak (PRP) type conjugate gradient method. We show that the
FCG method with some Armijo-type line search is globally convergent. Our
numerical experiments indicate the promising performance of the proposed
method.
