The physical quantities develop with critical behavior near the (quantum) critical regime of correlated systems, such as superfluid density of two dimensional superconductor, surface critical behavior in topological phase, Higgs mode in quantum antiferromagnet, quantum criticality in multiferroics, quantum phase transition in two-dimensional electron system, etc. Despite the variety of complex interactions and correlations, the critical behavior only depends on global properties such as the spatial dimension, the symmetry of the order parameter, and the range of interaction. Recently we found a new quasi-one-dimensional chain compound NiTe₂O₅, in which spin-1 of Ni²⁺ ions form a one-dimensional chain structure through NiO₆ octahedra’s edge-sharing. Although it undergoes a long-range antiferromagnetic (AFM) order with an archetypical anisotropic AFM anomaly at T_N = 30.5 K, the AFM order parameter develops with intriguing unconventional critical exponents. In this talk, we present magnetic properties and structure of NiTe₂O₅ and discuss its unconventional critical behavior.