Continuous phase plate (CPP) is a typical phase optical element. It will form a speckle field focused by a lens. The statistical characteristics of the speckle field affect the beam smoothing result. When a lens with large number aperture is used, scalar diffraction theory is unsuitable to analyze the distribution character of the focal spot because the paraxial approximation is no longer valid. In this paper, the Richar-Wolf vector diffraction theory is employed to calculate the focal spot of CPP under the strong focusing condition. Then both the profile of the focal spot and its statistical characteristics are discussed in detail. The results show that the spot size that calculated by the vector method is larger than which calculated by scalar method due to the non-paraxial effect. According to the feature of the vector method, the z-component of the light field can be obtained. The amplitude distribution of the speckle meets the Rayleigh distribution character, and its intensity distribution meets the negative exponential distribution character. Influenced by the z-component, the intensity distribution in the vectorial resultant direction will slightly deviate from the negative exponential distribution character .