Nonlinear optical crystals generally hold the intrinsical contradiction between the laser damage threshold and transmission range, which restricts the development of the high-power and large-energy mid-infrared (mid-IR) lasers, especially the mid-IR optical parametric chirped-pulse amplification (OPCPA) system. The langasite crystal was identified as a promising candidate for the 4-6 mu m terawatt-class OPCPA system but suffers from the relatively low effective nonlinear optical (NLO) coefficient (deff). Herein, a birefringence dispersion management strategy is originally developed and applied for the deff improvement of langasite crystals based on their structural symmetry, and a series of La3(Nb1-xTax)0.5Ga5.5O14 (LGNTx) solid-solution crystals (x = Ta/(Ta + Nb) = 0.17, 0.40, 0.51, 0.77, and 0.95) were theoretically designed and grown for the first time. By characterization of the crystals, the LGNT0.40 crystal was experimentally confirmed with the largest deff by implementing a data-driven routine, which is 1.7 times improvement compared with that of the well-known La3Nb0.5Ga5.5O14 (LGN) crystal and 2.9 times of theoretical enhancement in the amplification efficiency of the OPCPA system. In addition, their crystalline phase, stoichiometric ratios, and rocking curves were comprehensively evaluated. These results do not only provide a kind of candidate for the ultra-intense mid-IR lasers but also demonstrate a feasible strategy for managing the birefringence dispersion applied in the optics, including polarization regulation, beam splitting, wave plates, etc.