The first runway to be destroyed was 15km (nine miles) from the Colombian border in the state of Apure.
Venezuela is often used as a transit point by traffickers sending Colombian cocaine to the US and Europe.
Washington has criticised Venezuela for not doing enough to combat the cocaine trade - a charge Venezuela denies.
The US state department, in its annual drugs report published in March, described Venezuela as one of the principal drug transit countries in the Western Hemisphere.
It accused the Venezuelan authorities of failing to co-operate fully in the international fight against drugs.
Success in tackling the illegal drugs trade in Colombia, the report said, was leading to a shift in trafficking patterns to countries like Venezuela, which suffer rampant high-level corruption and a weak judicial system.
The Venezuelan government rejects this, pointing to a number of initiatives and major seizures as proof that it is cracking down on the illegal trade.
The vast area of Los Llanos, which stretches east from the Colombian border, is very flat, making it ideal terrain for traffickers who can easily create improvised runways.
In the state of Apure state alone, Venezuelan authorities have found 157 landing strips and they estimate that there are hundreds more.
The objective of the bombing missions is to destroy them all, officials say.
Colonel Nestor Reverol, the director of Venezuela's National Anti-Drugs Office, says their action is proof of the country's commitment to tackling the drugs trade.
"We are fulfilling our responsibility in the war against this scourge," he said.
The authorities say the bombing operation will be backed up by a awareness and social programme aimed at the indigenous communities living in these remote parts of the country.