We consider the problem of self-calibrating a moving camera which is equipped with a zoom lens. This consists essentially in estimating the 5 intrinsic parameters of the pinhole camera model. However, these parameters are not independent. Thus, we propose to do a pre-calibration of the camera, with the aim to model the interdependence of the intrinsic parameters. We show that self-calibration then comes down to the estimation of only 1 intrinsic parameter. We propose a method which exploits this and which does not need an initialization of the intrinsic parameters. The method consists mainly in finding the closest common root of several low-degree polynomials. Besides the simple computations needed, it is easy to parallelize and thus well suited for future real-time application. The improvement of our method on self-calibration without pre-calibration is shown by experiment.