I ploted histogram of unadjusted p-value. I encounted a huge peak at p-value=1, anybody knows the reason? Is it because the zero counts? How can I verify that?

hist(top.table.edgeR$PValue, breaks=100, main="",xlab="Unadjusted P values", col="lightblue")

Thanks for your help!

Yes, it is almost certainly because of genes for which all the counts are zero or very small.

A gene with no counts at all will naturally yield a p-value=1. Other very low counts will also give p-values=1 when the counts are as balanced as possible between the two experimental conditions. If you have a huge peak at p-value=1, it is probably because you haven't filtered out genes with consistently small counts.

Note that the exactTest() in edgeR will always give some over-representation of p-values equal to 1, because this is a property of exact tests. So you will usually get a peak at the 1 even when the analysis is done perfectly. If the peak is very large though, it is probably because you haven't filtered. We always recommend that users filter out genes with very small counts -- there is no point in keeping them in the analysis.