Levene’s test checks the homogeneity of variance assumption, not the normality assumption.
If Levene’s test shows that your data violates the homogeneity of variance assumption, then you have the following choices:
– make sure that the homogeneity of variance assumption isn’t being being violated because of outliers; if so you need to deal with the outliers first
– perform a one-way analysis instead using Brown-Forsythe or Welch’s test, which do not require homogeneity of variances
– transform the data to try to eliminate the problem. Typical transformations are log(x), x^2, 1/x