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Demonstrated by the first principles calculation and the angle-resolved photoemission spectroscopy (ARPES) measurement, the transition-metal pentatelluride ZrTe₅ is the prototype of massive Dirac material close to the topological critical point. Many exotic and anomalous behaviors of electric and thermoelectric transport were revealed recently in this system. Resistivity in ZrTe₅ exhibits a sharp peak at a finite temperature T_p. The peak occurs approximately at a large range of temperatures from 50 to 200K, but the exact value varies from sample to sample. This resistivity anomaly is always accompanied by the sign change of the Hall and Seebeck coefficients around the transition temperature. We propose a theory of quasiparticles to address a series of anomalous behaviors measured in ZrTe₅. The negative longitudinal magnetoresistance in this system was observed in a series of experiments by different groups, and was shown the quadratic behavior of the magnetic field. Under pressure, ZrTe₅ undergoes a topological phase transition accompanied by the closing and reopening of the band gap. The quadratic coefficient of the magnetoconductivity also varies with the external strain. We propose a quantum magneto-transport theory based on Landau level representation different from the chiral anomaly mechanism to account for the quadratic behavior and the strain dependence of the magnetoconductivity in ZrTe₅.