Properties of the vortex state in helical p-wave superconductor are studied by the quasiclassical Eilenberger theory. We confirm the instability of the helical p-wave state at high fields and that the spin-polarized local density of states M(E, r) appears even when Knight shift does not change. This is because the vorticity couples to the chirality of up-spin pair or down-spin pair of the helical state. In order to identify the helical p-wave state at low fields, we investigate the structure of the zero-energyM(E = 0, r) in the vortex states, and also the energy spectra of M(E, r).