Jensen was born in Århus. In 1960 he was the winner of the individual Nordic Championship, as well as a member of the Danish team that won the silver medal in the team time trial at that event. The Olympic100 km team time trialroad race was held in over 40-degree heat on Viale Cristoforo Colombo in Rome. One of the four-man Danish team, Jorgen B. Jorgensen, dropped out of the race due to sunstroke after the first lap, necessitating that all three remaining Danish cyclists finish the race for the team not to be disqualified. Jensen told his teammates that he felt dizzy. Niels Baunsøe clutched his jersey, keeping him from falling, while Vagn Bangsborg held Jensen from the other side. Bangsborg sprayed Jensen with water, leading to an apparent improvement, but when Baunsøe let go, Jensen collapsed and fractured his skull on the pavement. Jensen was brought by ambulance to an overheated military tent near the finish line, where he died that afternoon without regaining consciousness. Prince Axel of Denmark, an International Olympic Committee member, was on his way to Jensen's bedside when Jensen died. Oluf Jorgensen, the Danish cycling team's trainer, told Danish government investigators that he had given Jensen and some other cyclists Roniacol, a vasodilator. Jensen's autopsy was conducted at the Instituto di Medicina Legale. On 25 March 1961, the three Italian physicians who performed the autopsy submitted a final report stating that Jensen's death was caused by heatstroke, and that no drugs were found in his body. The complete autopsy report was never made public. Years later, Alvaro Marchiori, one of the doctors who conducted the autopsy, claimed that they had "found traces of several things", including amphetamine. Jensen's death led the InternationalOlympic Committee to form a medical committee in 1961 and institute drug testing at the 1968 Winter Olympics in Grenoble, France, and at the 1968 Summer Olympics in Mexico City, Mexico. Jensen was married to the niece of former Olympic cycling champion Henry Hansen. His family received one million lire from an Olympic insurance policy in compensation for his death.
