However, Smith, of Bitterne Road East, refused to accept his wrongdoings.
Instead, he insisted he had not meant to harm the child – who the court heard was now suffering from suicidal thoughts.
He denied all charges against him, but was found guilty during a six day trial at Southampton Crown Court.
Sentencing him, Judge Nicholas Rowland, said Smith had shown a lack of remorse.
He said: “What is apparent to me is the impact this has had on your victim.
“You’ve no appreciation for what you did nor any remorse.”
Judge Rowland also condemned Mr Smith’s use of violence, describing him as a “bully”.
Prosecuting, Rufus Taylor told the court that the first incident had occurred when the child was between five and six-years-old.
The court heard how the assaults had caused “serious” psychological harm to Smith’s victim.
Defending, Sarah Jones said Smith had come from a violent background and accepted her client faced a lengthy prison sentence.
Judge Rowland sentenced Smith to a total of 15 years in prison.
His sentence was for four multiple counts of rape, as well as concurrent sentences for sexual assault and cruelty to a child.
Smith was also given a further concurrent sentence for attempting to pervert the course of justice.


Police in Thailand have arrested an elderly Canadian man who media reports say was part of a secret cabal of foreign pedophiles who preyed on young teenage boys in the resort city of Pattaya.
Eddy Walsh, 71, was busted for molesting a 13-year-old boy. He has denied the charge.
It wasn’t immediately known where Walsh is from in Canada, but sources told Tnews that the pensioner hung around a group of European retirees who engaged in sexually molesting children.
One of the men was a condo manager.
Walsh was arrested outside the hotel Yen Sabai Mansion in central Pattaya. A warrant for his arrest had been issued.
The victim’s mother said her son was taken to a room in the hotel and molested as a video camera recorded.
Cops say that inside the third-floor room they discovered a treasure trove of “obscene videos.” They also seized a phone, tablet, computer notebook and some clothes.
Investigators plan to test the DNA related to the boy at the centre of the molestation of a child under 15 charge.
Walsh was interviewed in the presence of a Canadian Embassy staff member.