She loved him
Before we get down to the details of it, it is worth noting that it may not have been a romantic love, especially considering she was aware of Renly's... orientation.
In this conversation with Podrick she shows a great deal of admiration for the man and at the emphasised bit at the end even admits to loving him.
PODRICK: You weren't a knight, but you were a Kingsguard to Renly Baratheon, weren't you?
BRIENNE: I was.
PODRICK: Lord Tyrion said he was a good man.
BRIENNE: He was.
PODRICK: But how did you end up serving Renly?
BRIENNE: (After a few moments). When I was a girl, my father held a ball. I'm his only living child, so he wants to make a good match for me. He invited dozens of young lords to Tarth. I didn't want to go, but he dragged me to the ballroom. (Pauses). And it was wonderful. None of the boys noticed how mulish and tall I was. The shoved each other, and threatened to duel if they thought it was their turn to dance. And whispered in my ear how they wanted to marry me and take me back to their castles. (Smiles). My father smiled at me and I smiled at him. I'd never been so happy. (Her smile drops). Till I saw a few of the boys sniggering. And then they all started to laugh, they couldn't keep the game going any longer. They were toying with me. ‘Brienne the Beauty’, they called me. Great joke. And I realized I was the ugliest girl alive. A great lumbering beast. I tried to run away, but Renly Baratheon took me in his arms. “Don't let them see your tears,” he told me. “They’re nasty little shits. The nasty little shits aren't worth crying over.” He danced with me and none of the other boys could say a word. And he was the king's brother after all.
PODRICK: But wasn't he... Lord Tyrion said he was...
BRIENNE: Yes, Pod, he liked men, I'm not an idiot. He didn't love me, he didn't want me, he danced with me because he was kind and he wouldn't see me hurt. He saved me from being a joke. From that day until his last day. And I couldn't save him in return. Nothing's more hateful than failing to protect the one you love. One day, I will avenge King Renly.
Game of Thrones, Season 5 Episode 3, “High Sparrow”
However, in the books it is certainly a lot more explicit and she certainly loved him. Considering, as far as I’m aware, Brienne and Renly’s relationship is pretty much the same between the two canons I’d say it’s worth mentioning.
"That is a lie." Renly Baratheon had been more than a king to her. She had loved him since first he came to Tarth on his leisurely lord's progress, to mark his coming of age. Her father welcomed him with a feast and commanded her to attend; elsewise she would have hidden in her room like some wounded beast. She had been no older than Sansa, more afraid of sniggers than of swords. They will know about the rose, she told Lord Selwyn, they will laugh at me. But the Evenstar would not relent.
A Feast for Crows, Brienne I
Lord Renly was ahead of her, her sweet smiling king. He was leading her horse through the trees. Brienne called out to tell him how much she loved him, but when he turned to scowl at her, she saw that he was not Renly after all. Renly never scowled. He always had a smile for me, she thought... except...
A Feast for Crows, Brienne VIII