Ever since he was first introduced in Dragon Ball Z: Battle of Gods back in March 2013, Dragon Ball fans around the world have speculated over how strong Beerus truly is. The God of Destruction for Universe 7 made quick work of every Z Fighter in his debut, including Goku at the Super Sayian God level, and even throughout Dragon Ball Super his strength has been unrivaled by almost ever being in the Dragon Ball Universe. So with each powerful character's introduction, fans are bound to ask how'd they'd stack up against almighty cat god.
Next up to the plate is the Grand Supreme Kai, also known as Daikaioh and/or the Great Lord of Lords. For those who haven't been keeping up with the Dragon Ball Super manga, the Kai was able to seal away the energy-absorbing wizard Moro 10 million years ago. And when Moro escaped, the Galactic Patrol captured Majin Buu and reawakened the Grand Supreme Kai in order to help the patrol, as well as Goku and Vegeta, defeat Moro once again. The latest chapter of the manga showed he was able to give Buu the power to take on Moro in a fight (before the Namekian Dragon Balls got involved, that is), and he eventually swapped places with Buu's consciousness in order to help the others.
So could he take on Beerus? Well the answer isn't as cut and dry as you'd might think. Beerus made Majin Buu (which you'll remember, is the form where the Grand Supreme Kai has been absorbed by Buu) into a punching bag in both Battle of Gods and the retelling in Dragon Ball Super. The version of Buu that fought Moro on New Namek was clearly a more capable fighter, but you have to remember that his main advantage was being immune to Moro's magic, which wouldn't play any role into trying to take on Beerus' God Ki.
But let's try removing Buu from the equation and just consider him when he had his own body as the Grand Supreme Kai. The events of Dragon Ball Z showed us that he was unable to outright kill Kid Buu (who had already absorbed South Kai), leading to his absorption. And since we know Beerus outclasses Kid Buu by quite a margin, that means Grand Supreme Kai likely wouldn't have lasted long in a fight against him.
The only version of the Grand Supreme Kai that might have stood a small chance against Beerus was prior to his first fight with Moro. As the Dragon Ball Wiki states, he had to give up most of his godly powers in order to defeat Moro the first time, which likely means he was still weakened once he eventually fought Kid Buu. Unfortunately, we may never know how truly strong he was in the years before that encounter.
So what's the verdict? Based on everything we know and everything we've seen in both the manga and anime, the Grand Supreme Kai would not be able to defeat Beerus.