In this paper, we are concerned with the existence of ground state solution for the following fractional differential equations with tempered fractional derivative: (Formula presented.) where α∈(1/2,1), λ>0, Dα, λ± are the left and right tempered fractional derivatives, Wα, 2(ℝ) is the fractional Sobolev spaces, and f ϵ C(ℝ×ℝ,ℝ). Assuming that f satisfies the Ambrosetti–Rabinowitz condition and another suitable conditions, by using mountain pass theorem and minimization argument over Nehari manifold, we show that (FD) has a ground state solution. Furthermore, we show that this solution is a radially symmetric solution. Copyright © 2017 John Wiley & Sons, Ltd.