David McWhinnie, 49, hurled abusive remarks at the politician while she was canvassing in the East End of Glasgow - the area she represents in Parliament.
Mrs Curran, 55, was abused by McWhinnie in the city's Amulree Street in Shettleston.
Police were flagged down to attend the incident but McWhinnie continued to shout and swear.
At Glasgow Sheriff Court McWhinnie pleaded guilty to behaving in a way that would cause a reasonable person to suffer fear or alarm by shouting, swearing and uttering offensive remarks towards Mrs Curran, on November 23, last year.
He also admitted placing others in a state of fear and alarm by threatening his elderly parents on Culrain Street, also in Shettleston, on December 14, 2013 and days later on December 18, stealing a bicycle from Hill Street in Glasgow city centre.
Sheriff John Beckett QC jailed McWhinnie for a total of 328 days.
Mrs Curran has been an MP for Glasgow East since 2010 and is currently Shadow Secretary of State for Scotland.