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The detection of high-energy neutrino coincident with the blazar TXS 0506+056provides a unique opportunity to test Lorentz invariance violation (LIV) in theneutrino sector. Thanks to the precisely measured redshift, i.e., $z=0.3365$,the comoving distance of the neutrino source is determined. In this work, weobtain and discuss the constraints on the superluminal neutrino velocity$\delta_\nu$ and the LIV by considering the energy loss of superluminalneutrino during propagation. Given superluminal electron velocity ($\delta_e\ge 0$), a very stringent constraint on superluminal neutrino velocity can bereached, i.e., $\delta_\nu \lesssim 1.3\times 10^{-18}$, corresponding to thequantum gravity (QG) scale $M_{\rm QG,1} \gtrsim 5.7 \times 10^{3} M_{\rm Pl}$and $M_{\rm QG,2} \gtrsim 9.3 \times 10^{-6} M_{\rm Pl}$ for linear (quadratic)LIV, which are $\sim 12$ orders of magnitude tighter for linear LIV and $\sim9$ orders tighter for quadratic LIV compared to the time-of-flight constraintfrom MeV neutrinos of SN 1987A. While given the subluminal electron velocity, aweaker constraint on the superluminal neutrino velocity is obtained, i.e.,$\delta_\nu \lesssim 8 \times 10^{-17}$, which is consistent with theconclusions of previous works. We also study the neutrino detection probabilitydue to the distortion of neutrino spectral shape during propagation, whichgives slightly weaker constraints than above by a factor of $\sim2$.

Limiting Superluminal Neutrino Velocity and Lorentz Invariance Violation by Neutrino Emission from the Blazar TXS 0506+056