The Celtic captain is delighted by the progress that the striker is making right now.
Griffiths took a well documented break from football in December of last year to deal with off the pitch personal problems, missing the second half of the 2018/19 season.
Working hard to fight his way into Neil Lennon's plans for the new campaign, the Scotland international has looked in excellent form in the early stages of the season.
Brown thinks it's just a glimpse of what's to come from the 28-year-old.
As quoted by BBC Scotland, the Hoops skipper said: "To get back to that fitness level, for him to get back to that belief as well that every shot that he's going to hit is going to go in the back of the net because he is one the best finishers I've ever seen.
"He's getting fitter, he's getting sharper, he's getting stronger on that left foot. We all know it's a wand."
With three goals and an assist in five appearances this summer (Transfermarkt), Griffiths is certainly showing a desire to become a main man for the Scottish champions once again.
Whether starting in a relief role for Odsonne Edouard or coming off the bench for the Frenchman, the forward is set to play a crucial role in Lennon's squad across 2019/20.
Given Brown thinks his progress in training is set to pay even bigger rewards then Celtic fans could be in for a real treat.
If he gets the minutes, he'll get the goals.
It'll be big for Edouard too. He carried the Hoops on his back at times towards the end of last season. If he can be rested and substituted off more often then it'll only make him fresher for the biggest tests.
With Bayo on his way back too, Celtic have a strike force that should make them competitive at home and abroad.
Have something to tell us about this article?