Semi-bent functions have almost maximal nonlinearity. In this paper, two classes of semi-bent functions are constructed by modifying the supports of two quadratic Boolean functions $f_1(x_1,x_2,cdots,x_n)=igopluslimits^{k}_{i=1}x_{2i-1}x_{2i}$ with $n=2k+1geq3$ and $f_2(x_1,x_2,cdots,x_n)=igopluslimits^{k}_{i=1}x_{2i-1}x_{2i}$ with $n=2k+2geq4$. Meanwhile, the algebraic normal forms of the newly constructed semi-bent functions are determined.