In this communication, a new design of low-profile angle-selective surfaces (ASSs) is proposed. By utilizing the first odd mode resonance of a frequency-selective surface (FSS), a single-layer ASS can be designed. For this purpose, the structure of the unit cell has been chosen carefully and its dimensions are optimized. Furthermore, to effectively analyze and optimize the performance of the ASS, an improved simplified partial element equivalent circuit (PEEC) model for periodic structure considering the skin effect is developed, which can significantly accelerate the calculation of the scattering coefficients. The results calculated by the proposed PEEC agree well with those simulated by the simulation software. Based on the first odd mode resonance, two ASSs have been designed by using the improved simplified PEEC to accelerate the calculation. Their thickness is less than $0.0098 \lambda $ , where $\lambda $ is the wavelength corresponding to the operating frequency of 5.8 GHz. To verify the design, a prototype of one designed ASS has been fabricated and measured. The simulated and measured results are in good agreement with an angular passband ( $\text{S}21\ge -1$ dB) of less than 4° and an angular stopband ( $\text{S}21\le -20$ dB) of greater than 30° at the operating frequency.