And he insists it was good news for the Premier League when the Liverpool striker stayed in England following the biting incident last season which saw him suspended for 12 matches.
On Saturday at Anfield Jol's side will come up against the controversial player who was his captain when he managed Ajax in Holland.
Jol insisted on keeping Suarez as his skipper following the Uruguayan's first biting episode, when he bit PSV Eindhoven's Otman Bakka in 2010, an incident which saw him suspended for seven matches.
And he maintains that English football has not seen the real character of Suarez, who also infamously helped Uruguay to beat Ghana in the 2010 World Cup when he handled the ball on the line to save a certain goal with Ghana missing the resultant penalty.
Jol said: "He's a lot different off the pitch. He's actually quiet. He's not outspoken. He's not someone who will fight people but on the pitch he wants to win.
"I can remember in the World Cup he saved the goal and it was ridiculous because he was like the goalkeeper and then there was a penalty and he was sent off and then he was cheering when they missed it.
"He's a winner. He's a team player. That is the great thing. It's not about him. He's always happy for his team and for other players to do well. That is the strange thing because normally they have a big ego but he's a good boy."
In a comparison with Manchester City's Sergio Aguero, Jol would take Suarez every time.
Jol said: "His agent is the brother of (former Barcelona manager) Pep Guardiola so he was always linked with Barcelona.
"When he was at Ajax we thought he would go to Barcelona. He went to Liverpool and when Luis stayed I knew for a fact he was behind it because otherwise he would have been on his bike.
"There is no-one better than him in the box. If he's in the box with the ball you can't stop him because he goes through you or he loses the ball or he goes to goal and he scores.
"Aguero is more technical. Suarez, with me, scored 53 goals in one year and I don't know if Aguero is good enough to say he could do the same.
"Suarez is always in the top three as a top scorer. He can play as a number nine or a second striker. He can play on the flank as well. If you judge a forward player on his goals I'm not sure there is a second one like him. It was good for the Premier League (that he stayed)."
Jol, whose side lie 16th and two points off the relegation zone, has to decide whether to play Norwegian central defender Brede Hangeland, who has been suffering from a sciatic nerve problem while Bryan Ruiz, who suffered booing when he was substituted in the defeat against Manchester United last Saturday, has a back niggle.
Fulham will be without right back Sascha Riether, who starts a three-match ban after being found guilty of violent conduct by the Football Association for stamping on United's Adnan Januzaj.
Jol's biggest problem, however, will be Suarez, even though he has briefed his defenders about the striker.
"I tell them what I know of him," said Jol. "But it's about my players. Can they defend what he intends to do? He is off the cuff, quite impulsive. It is not easy to defend against him because he is unpredictable."