We investigate the large time behavior of the global weak entropy solutions to the symmetric Keyfitz-Kranzer system with linear damping. It is proved that as<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>t</mml:mi><mml:mo>→</mml:mo><mml:mi>∞</mml:mi></mml:math>the entropy solutions tend to zero in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>norm.