By using the density-matrix renormalization group method, the spin entanglement in the antiferromagnetic Heisenberg chain with the staggered Dzyaloshinskii-Moriya (DM) interactions is investigated. It is found that the staggered DM interactions remove the field-induced second order quantum phase transition of the system at the magnitude of magnetic field H＝2, and lead to the vanishing of the anomalous behavior of quantum entanglement. Also, the staggered DM interactions eliminate the divergence of entanglement range. It means the disappearance of the factorizing point in the model studied. Due to the presence of the staggered DM interactions, the system will never come to the state of saturated ferromagnetism under finite magnetic fields, thus maintaining the spin entanglement. The staggered DM interactions favor the tuning of the strength and range of spin entanglement.