In this article, the near field of a two-dimensional infinite near-field focusing antenna with Gaussian taper excitation is determined. By Gabor representation, any slowly varying excitation of array antenna can be expanded to series of Gaussian taper excitation. To achieve the Gaussian taper excitation, the focus point of a two-dimensional infinite near-field focusing antenna is placed in complex space. By adopting the Poission sum formula, radiation fields of this type antenna are transferred to terms of Floquet modes. Asymptotic evaluation technique is utilized to calculate the Floquet mode integral in closed form. Results of asymptotic evaluation are compared with those obtained by direct numerical integral, and good agreement is achieved.