In 2018, Cong and Zhao introduced noncash risk measures with 1-norm for weak cone-type acceptable sets. In the present paper, we take a further look at nonconvex, noncash risk measures with p-norm (1 ≤ p ≤ ∞) for nonweak cone-type acceptable sets. A convex extension of the nonconvex, noncash risk measures is given and a representation theorem of a convex extension of the nonconvex, noncash risk measures is achieved.