  Motivated by applications in DNA-based storage and communication systems, we
study deletion and insertion errors simultaneously in a burst. In particular,
we study a type of error named $t$-deletion-$s$-insertion-burst ($(t,s)$-burst
for short) which is a generalization of the $(2,1)$-burst error proposed by
Schoeny {\it et. al}. Such an error deletes $t$ consecutive symbols and inserts
an arbitrary sequence of length $s$ at the same coordinate. We provide a
sphere-packing upper bound on the size of binary codes that can correct a
$(t,s)$-burst error, showing that the redundancy of such codes is at least
$\log n+t-1$. For $t\geq 2s$, an explicit construction of binary $(t,s)$-burst
correcting codes with redundancy $\log n+(t-s-1)\log\log n+O(1)$ is given. In
particular, we construct a binary $(3,1)$-burst correcting code with redundancy
at most $\log n+9$, which is optimal up to a constant.
