Juvenile Mentoring Program Act of 2010 or JUMP Act of 2010 - Amends the Juvenile Justice and Delinquency Prevention Act of 1974 to direct the Administrator of the Office of Juvenile Justice and Delinquency Prevention to award grants to and enter into contracts with state and local educational agencies or nonprofit organizations to implement mentoring programs that link at-risk youth with responsible adults who, on a one-to-one volunteer basis, provide such youth with supportive relationships and exposure to new experiences that enhance their ability to become responsible citizens.

Defines an "at-risk youth" as an individual under age 18 who is at risk of educational failure or involvement in delinquent activities.

Requires the Administrator to develop and distribute to program participants specific model guidelines for screening prospective program mentors.

Gives grant priority to applicants that: (1) serve at-risk youth in high crime areas; and (2) have at least 60% of their youth eligible to receive funds under the Elementary and Secondary Education Act of 1965.