The Minot Daily News reports that 28-year-old Omar Mohamed Kalmio declined to comment following the sentencing.
Judge Douglas Mattson sentenced Kalmio to four consecutive terms of life in prison without the possibility of parole.
Kalmio was convicted of fatally shooting 19-year-old Sabrina Zephier at her home then killing her mother, her 13-year-old brother and her mother's boyfriend at a nearby home in January 2011.
The baby girl was found unharmed.
Kalmio, who had a history of violent crime, was working in North Dakota's oil patch at the time and said he was in the US under political asylum.