A method for generating vector beams with higher-order states of polarization based on a setup with a one phase-only liquid crystal spatial light modulator is proposed. The polarization properties and double-slit interference of the higher-order vector beams were investigated in detail. The cross section intensity distributions were flower-like for higher-order vector beams when passing through a linear polarizer. Misplacements appeared in the double-slit interference fringes, which divided each fringe into several discrete parts, i.e., 2P-1 for P≥2, and 3 for P=1, where P is the polarization order number. When associated with optical petal orientations analysis of the beam spots behind a linear polarizer, the double-slit interference can be used to detect and analyze higher-order vector beams.