A new C-type subhierarchy for KP hierarchy with two new time series γn and σk ( (Tn,crk )-CKPH), which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. The zero-curvature representation for the (γn, σk )-CKPH is derived. The reduction and constrained flows of (γn, σk )-CKPH are studied.