How to draw the boxplot with significant level?

I don't quite understand what you mean by boxplot with significant level but here a suggestion how you can generate those bars: I would solve this constructing small dataframes with the coordinates of the bars. Here an example:

pp <- ggplot(mtcars, aes(factor(cyl), mpg)) + geom_boxplot()
df1 <- data.frame(a = c(1, 1:3,3), b = c(39, 40, 40, 40, 39))
df2 <- data.frame(a = c(1, 1,2, 2), b = c(35, 36, 36, 35))
df3 <- data.frame(a = c(2, 2, 3, 3), b = c(24, 25, 25, 24))

pp + geom_line(data = df1, aes(x = a, y = b)) + annotate("text", x = 2, y = 42, label = "*", size = 8) +
     geom_line(data = df2, aes(x = a, y = b)) + annotate("text", x = 1.5, y = 38, label = "**", size = 8) +
     geom_line(data = df3, aes(x = a, y = b)) + annotate("text", x = 2.5, y = 27, label = "n.s.", size = 8)

I know that this is an old question and the answer by DatamineR already provides one solution for the problem. But I recently created a ggplot-extension that simplifies the whole process of adding significance bars: ggsignif

Instead of tediously adding the geom_line and annotate to your plot you just add a single layer geom_signif:

library(ggplot2)
library(ggsignif)

ggplot(iris, aes(x=Species, y=Sepal.Length)) + 
  geom_boxplot() +
  geom_signif(comparisons = list(c("versicolor", "virginica")), 
              map_signif_level=TRUE)

Full documentation of the package is available at CRAN.