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In this paper, with the help of variational approach, the fundamental soliton solutions are derived in nonlinear Schrödinger equation which describes an optical medium with cosine-oscillation nonlocal nonlinearity. The relationships between the nonlocal parameters of the medium and the soliton parameters, such as the amplitude, the phase and the power of the fundamental soliton, are given. The influence of nonlocal parameters and soliton parameters on soliton properties is discussed in detail, and the role of each parameter is illustrated.