  In this paper, we study a class of infinite simple Lie conformal algebras
associated to a class of generalized Block type Lie algebras. The central
extensions, conformal derivations and free intermediate series modules of this
class of Lie conformal algebras are determined. Moreover, we also show that
these Lie conformal algebras do not have any non-trivial finite conformal
modules. Consequently, these Lie conformal algebras cannot be embedded into
$gc_N$ for any positive integer $N$.
