* Corn futures rises for 4 of 5 sessions on Chinese demand

* Soybeans, wheat firm after closing lower in previous session

SINGAPORE, Sept 22 (Reuters) - Chicago corn futures bounced back on Tuesday, after suffering their biggest one-day loss in almost seven weeks in the previous session, as expectations of strong Chinese demand supported prices.

Still, improved U.S. crop ratings and harvest pressure kept a lid on prices.

"Chinese demand is supportive for prices, but overall there is no shortage of grains in the world at the moment," said Ole Houe, director of advisory services at agriculture brokerage IKON Commodities in Sydney.

The most-active corn contract on the Chicago Board of Trade (CBOT) rose 0.2% to $3.70-1/2 by 0332 GMT, after dropping 2.3% in the last session, the biggest daily loss since Aug. 4.

Soybeans added 0.3% to $10.26 a bushel and wheat gained 0.5% at $5.57-1/2 a bushel.

While soybeans jumped to their highest in more than two years last week, corn hit a six-month top as China has stepped up purchases of U.S. products with a recovery in demand for animal feed.

The USDA said private exporters reported the sale of 132,000 tonnes of soybeans to China. There were also soybean sales to Pakistan and unknown destinations.

Condition ratings for the U.S. corn crop improved during last week and soybean ratings held steady, while the harvest of both crops was underway, the U.S. Department of Agriculture (USDA) said after the market closed on Monday.

The USDA rated 61% of the corn crop in "good-to-excellent" condition, up from 60% a week earlier, bucking analyst expectations for a 1-point decline.

High demand from importers and concerns over the winter harvest drove Ukraine's 2020 export prices for 12.5% protein milling wheat around $9 per tonne higher over the last week, APK-Inform agriculture consultancy said on Monday.

In the wheat market, the focus is on a tender issued by Egypt, the world top buyer of the grain, to buy an unspecified amount of wheat from global suppliers for shipment Nov. 21-30.

Commodity funds were net sellers of CBOT corn, wheat, soybean, soyoil and soymeal futures contracts on Monday, traders said. (Reporting by Naveen Thukral, Editing by Sherry Jacob-Phillips)