The phrase "strong grudge" is correct and usable in written English.
It can be used to describe a deep and intense feeling of resentment or anger towards someone. Example: After years of mistreatment from her boss, Jane held a strong grudge against him and refused to speak to him at company events.
While Johnny would eventually marry Linda, Joey held a strong grudge against them both, and, though they continued to perform and tour together, the two rarely talked to each other.
In early July, LSU coach Les Miles stirred inter-conference controversy when he publicly criticized USC's 2007 schedule in front of LSU boosters; though the two schools had not played each other since 1984, the LSU Tiger faithful maintained a strong grudge against the Trojans after they shared the national title in the controversial 2003 season.
Although there are sub-Saharan Africans who hold strong grudges against America (Somalis, for instance, in whose country America carried out a clumsy intervention, or Rwandans, whose rescue it stood back from), it seems improbable that such people would be prepared or equipped to exact so co-ordinated a revenge.
What starts out as a petty argument over a trivial issue can turn into someone bearing a strong personal grudge against you.
The result is a strong propensity for holding grudges.
Such talk keeps your grudges light and strong, the way God intended.
This section is not easy and its not really meant to be - you have to be strong enough to transcend any grudges you have and overcome ill will.
His obsession with Megyn Kelly indicates he is weak, not strong, and that he holds a grudge.
We kind of got back to a point of no grudge for the moment, and he was being strong and wonderful.
This is not a grudge match: neither fighter seems to have any strong feelings about the other, which means that the promoters are in the unusual position of having to sell this boxing match as a purely athletic event.
When some press outlets — including this newspaper — continued to mention his past, Black's strong sense of Southern honor was offended, and he bore a grudge for decades.
