Abstract: In this poper, we study the numerical solution of the first-kind Fredholm integral equation
∫_-1¹ k(t,s)y(s)ds=f(t),t∈[-1,1]
where f(t) is continuous and k(t, s) may be weakly singular. The kernel k(t, s) is assumed to be expressed as k(t, s)=h(t, s)m(t, s), where h(t, s) is of a standard form for example h(t, s)=|t-s|^α, α>-1, and m(t, s) is continuous. By using Lagrange polynomial interpolation, a sequence of the approximate solution is established and the convergence is proved.