Catalysis by enzymes on surfaces has many applications. However, strategies for efficient enzyme immobilization with preserved activity are still in need of further development. In this work, we investigate polyelectrolyte brushes prepared by both grafting-to and grafting-from with the aim to achieve high catalytic activity. For comparison, self-assembled monolayers that bind enzymes with the same chemical interactions are included. We use the model enzyme glucose oxidase and two kinds of polymers: anionic poly(acrylic acid) and cationic poly(diethylamino)methyl methacrylate. Surface plasmon resonance and spectroscopic ellipsometry are used for accurate quantification of surface coverage. Besides binding more enzymes, the "3D-like" brush environment enhances the specific activity compared to immobilization on self-assembled monolayers. For grafting-from brushes, multilayers of enzymes were spontaneously and irreversibly immobilized without conjugation chemistry. When the pH was between the pI of the enzyme and the p Ka of the polymer, binding was considerable (thousands of ng/cm2 or up to 50% of the polymer mass), even at physiological ionic strength. However, binding was observed also when the brushes were neutrally charged. For acidic brushes (both grafting-to and grafting-from), the activity was higher for covalent immobilization compared to noncovalent. For grafting-from brushes, a fully preserved specific activity compared to enzymes in the liquid bulk was achieved, both with covalent (acidic brush) and noncovalent (basic brush) immobilization. Catalytic activity of hundreds of pmol cm-2 s-1 was easily obtained for polybasic brushes only tens of nanometers in dry thickness. This study provides new insights for designing functional interfaces based on enzymatic catalysis.