Let introduce the Sobolev-type inner product $$ \big<f,g\big>=\int^1_{-1}f(x)g(x)dx+N\big[f'(1)g'(1)+f'(-1)g'(-1)\big], $$ where $N\geq0$. In this paper we prove a Cohen type inequality for Fourier expansion in terms of the polynomials associated to the Sobolev inner product.