1. Approve sth (without of) = to accept a plan, proposal or application; e.g.

The use of the new drug has yet to be approved by the Medical Research Council.

2. Approve of sb/sth = to think that someone or something is good; e.g.

INCORRECT: Those who approve the death penalty claim that life imprisonment is not effective.
CORRECT: Those who approve of the death penalty claim that life imprisonment is not effective.

INCORRECT: Some husbands do not approve the idea of their wives having a job.
CORRECT: Some husbands do not approve of the idea of their wives having a job.