I was trying to analyze a data with negative values. Is it possible to use ANOVA in this case?
Certainly. Why not? The most usual ANOVA models assume normally distributed errors, and that introduces the possibility of negative values. The assumptions of the Gauss-Markov theorem are that errors have expectation $0$, all have the same variance, and are uncorrelated, and that doesn't rule out negative values and in some cases may necessitate them. I don't know of any ANOVA models that would assume all values are nonnegative. Sometimes one might have only positive values of a response variable and then do ANOVA with their logarithms as the response variable, but that response variable to which one applies ANOVA is not constrained to be nonnegative.