Business leaders have grown more confident about the economy, although they remain worried about a possible recession, according to a private survey.

The Conference Board, a business-financed research group, said its business confidence index rose to 58 during the second quarter from 51 during the first three months of the year.The index released Sunday, compiled from a survey of about 1,000 top executives, skidded to 47 in the last quarter of 1987, following the October stock market crash.

The latest survey found an increase in confidence among executives in nine of the country's top 15 manufacturing industries and five of 10 leading non-manufacturing industries, the Conference Board said in a news release.

Most of the survey respondents said the economy and their own industries are stronger now than before the crash, said Steven Malin, senior economist for the business research group.

"But anxiety about rising inflation and interest rates continues to dampen enthusiasm about prospects for the second half of 1988," Malin said.