Crosby, the second Principal of Salem Normal School, was born in Sandwich, New Hampshire on October 13, 1810. He was graduated from Dartmouth College, which he entered at the young age of thirteen. Prior to his selection to serve on the Massachusetts Board of Education in 1854, Crosby served on the faculty at Dartmouth and later as Superintendant of Public Schools in Newburyport, Massachusetts.

In 1857, he was appointed Principal of Salem Normal School. During his tenure at Salem, he continued to raise the school to a higher standard of excellence and contributed extensively to its library. He was an educational reformer in his time, putting less stress on the professional teacher-education courses and more stress on the liberal arts. He was also a reformer in a broader sense and was an ardent abolitionist and supporter of the rights of women. In 1864, he helped found the Salem Freedmen's Aid Society. After the Civil War ended, he left Salem Normal to edit The Right Way, a newpaper devoted to the equal rights of emancipated slaves. Crosby died on April 17, 1874, after a short illness.