James Veitch may refer to:

• James Veitch, Lord Elliock (1712–1793), Scottish advocate, judge, politician and landowner
• James Veitch (comedian), British comedian, director, writer and producer
• James Veitch (horticulturist) (1792–1863), English horticulturist
• James Veitch Jr. (1815–1869), English horticulturist
• James Herbert Veitch (1868–1907), English horticulturist
• James Veitch (minister) (1808–1879), minister of the Church of Scotland, astronomer and geologist
• James Veitch (rugby union), Scottish rugby union player