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Firstly, we show the almost everywhere pointwise convergence of Schr\\\"odinger equation in Fourier-Lebesgue spaces $\\hat{H}^{\\frac{1}{p},\\frac{p}{2}}(\\mathbb{R})(4\\leq p<\\infty),$ $\\hat{H}^{\\frac{3 s_{1}}{p},\\frac{2p}{3}}(\\mathbb{R}^2)(s_{1}>\\frac{1}{3},3\\leq p<\\infty),$ $\\hat{H}^{\\frac{2 s_{1}}{p},p}(\\mathbb{R}^n)(s_{1}>\\frac{n}{2(n+1)},2\\leq p<\\infty,n\\geq3)$ with rough data. 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