The former Manchester United midfielder believes that the Toffees can continue their winning ways against Stoke City at the Britannia Stadium
However, the Republic of Ireland international has acknowledged that it will be a difficult task considering the Potters' physicality and defensive capabilities.
"It's always a tough place to go because they're a very good team defensively, and physically they're obviously one of the biggest teams in the Premier League so they're a threat from set pieces," Gibson told evertontv.
"But we've been on a good run of form the last few games so hopefully if we can keep playing well I think we can go there and get a result."
The 25-year-old central midfielder recently returned to action for David Moyes' side after a being ruled out for three months with a thigh injury and has revealed his happiness with his own performances since resuming action.
He said: "Obviously to be out for three months, it was quite a long time. But I worked hard when I was out and I slotted back in straight away which was pleasing.
"I'm happy enough. Hopefully I can just keep it going now over the next few games," concluded the former Manchester United midfielder.