We propose a better algorithm for approximate greatest common divisor (approximate GCD) of univariate polynomials in terms of robustness and distance, based on the NewtonSLRA algorithm that is a solver for the structured low rank approximation (SLRA) problem. Our algorithm mainly enlarges the tangent space in the NewtonSLRA algorithm and adapts it to a certain weighted Frobenius norm. Moreover, we propose some improvement in computing time.