In this paper, the main aim is to introduce two classes HSp and HCp of p-harmonic mappings together with their corresponding subclasses HSp0 and HCp0, and investigate the properties of the mappings in these classes. First, we discuss the geometric properties of mappings belonging to HSp0 and HCp0, respectively. We prove that the image domains of the unit disk D under the mappings in HSp0 (resp. HCp0) are starlike (resp. convex). Secondly, extreme points for classes HSp0, HCp0, HSp∩Tp and HCp∩Tp are determined, where Tp denotes the set of all p-harmonic mappings with nonnegative coefficients. Finally, we establish the existence of the neighborhoods of mappings in HCp.