We have investigated the intrabinary shock emission from the redback millisecond pulsar PSR J2129-0429 with XMM-Newton and Fermi. Orbital modulation in X-ray and UV can be clearly seen. Its X-ray modulation has a double-peak structure with a dip in between. The observed X-rays are non-thermal dominant which can be modeled by a power-law with a photon index of ~1.2. Intrabinary shock can be the origin of the observed X-rays. The UV light curve is resulted from the ellipsoidal modulation of the companion. Modeling the UV light curve prefers a large viewing angle. The heating effect of the UV light curve is found to be negligible which suggests the high energy radiation beam of PSR J2129-0429 does not direct toward its companion. On the other hand, no significant orbital modulation can be found in gamma-ray which suggests the majority of the gamma-rays come from the pulsar.
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