It is narrated from Sayyiduna Ibn Umar (may Allah be pleased with them both) that the Prophet (peace and blessings be upon him) performed ramal (brisk walking) in the first three circuits of the Tawaf around the Ka'bah.
Hadith Referenceمسند احمد / مسند المكثرين من الصحابة / 5444
Hadith Gradingحکم دارالسلام:إسناده صحيح ، خ : 1617، م :1261.