It had started in the 1940's but it has increased the most in the 1970's.
Actually, the first GM foods were grown in California in the early 1990's. What the answer above was referring to was the Green Revolution which started in the 1940's, which was however the basis of GM foods. The Green Revolution was the start of HYV (similar to GM foods) which are High-Yielding varieties. These are genetically modified crops which have higher yields (in essence, you get more out of your crop).
Also, the first GM foods were sold in 1996.
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GMO crops were first approved in the late 1990s. GMO foods came on the commercial market not long after that.