He began skating at the age of four years. At the age of eleven he went to Saint Petersburg to train with Alexei Mishin, who also coached Yevgeny Plyushchenko. Then he coached from 2002 on the advice of Alexei Yagudin with Tatiana Tarasova. Later he moved again his trainer and trained with Jelena Wodoresowa.
2004 Gryazev won the Junior World Championships. In 2007 he was Russian champion in the seniors, but could not build on the international success of its predecessor. In the period from 2004 to 2007, he participated three times at World and European Championships, in 2005, he scored there with the eleventh and fifth place his best result. In 2009 he ended his competitive career.