The framework of Formaggia and Perotto (Numerische Mathematik 2001; 89:641-667) is considered to derive a new anisotropic error indicator for a Laplace problem in the energy norm. The matrix containing the error gradient is approached using a Zienkiewicz-Zhu error estimator. A numerical study of the effectivity index is proposed for anisotropic unstructured meshes, showing that our indicator is sharp. An anisotropic adaptive algorithm is implemented, aiming at controlling the estimated relative error. Copyright (C) 2003 John Wiley Sons, Ltd.