We investigate a new quadrature, namely the Gauss-Laguerre-like qua-drature, close to the Gauss-Laguerre quadrature, those whose weight function is modified from $z \longmapsto e^{-z}$ to $z \longmapsto (1 + e^{-z})^{-1}$. Firstly, we prove an explicit error formula for the Gauss-Laguerre and the Gauss-Laguerre-like quadratures, which apply to a subclass of holomorphic functions with isolated singularities outside of $]0 ; + \infty[$. Then, we explore the asymptotic of the respective error terms on two simple examples but sufficiently general to be meaningful for the reader. In order to control explicitly their relative error and to compute the related integrals, we also give explicit upper bounds of the error in these two examples.