In this talk, we introduce a family of infinite Lie conformal algebras B(k,l,p), which arise as semidirect sums of the Block type Lie conformal algebra B(p) and its nontrivial conformal modules from the Z-graded free intermediate series.  We provide a complete classification of all finite nontrivial irreducible conformal modules  over B(k,l,p) for any complex numbers k, l and nonzero p. As an application, we also obtain the classification of finite irreducible conformal modules over a series of finite Lie conformal algebras b(n) for n greater than 1.