This paper presents two planar convex hull algorithms on linear array. The First algorithm is for the case such thatn ≤ p, wherenandpare the number of points in S and the number of processors, respectively. The algorithm runs inO(n) which is optimal. The second algorithm is designed for a general case such thatn>p.The algorithm runs inO((n/p)log(n/p)) time, which is also optimal. Both algorithms have been extended tod-dimensional mesh-connected array withO(d2n1/d) in time for the case such asn < p,and O((n/p)log(n/p) + np1/d−1) in time for the case such asn>> p andp1/>> 2, which are both optimal.