Leeds were unbeaten during December, winning three and drawing two of their five league matches, and briefly climbed up to second place in the table.
Grayson, who collected his first manager of the month award, said: "I'm proud to have won it. A lot of hard work has gone in by my players and the rest of the staff.
"It's testament to the efforts of everyone and how hard we have worked over the past few weeks and months."
Source: PA
