Can I claim my grandson?He lived with me all year,didn't contribute to anything but he worked and made over $19,000.00?

to claim him as a qualifying child

these tests must be met.  i've excluded those that your statement answers 

the child must
1) be any of the following a) under age 19 at the end of the year b) a full-time student and under age 24 at end of the year c) or any age if totally and permanently disabled
2) Hasn’t provided over ½ his support
3) No joint return with the exception for a joint return filed only to claim a refund of tax withheld when neither spouse is required to file and no tax liability would exist for either spouse if separate returns were filed
4) Not be a qualifying child of another taxpayer with a higher priority under the tie-breaker rules

if he satisfies 1) above the next hurdle is support.  here's a link to the IRS support worksheet

https://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf

you may e able to determine the answer by just reading the lines without having to enter actual numbers.