Frequency estimation for single-tone complex sinusoidal signals under additive white Gaussian noise is a classical and fundamental problem in many applications, such as communications, radar, sonar and power systems. In this paper, we propose a new algorithm by interpolating discrete Fourier transform (DFT) samples. Different from other existing interpolation methods for frequency estimation, our algorithm is based on a much simpler expression and has mathematically tractable bias expression in closed form, which can potentially assist future bias correction. Simulations confirm that our proposed algorithm outperforms all existing alternatives in the literature with comparable complexity.