The large eddy simulation (LES) method coupled with the transported probability density function (PDF) turbulent-combustion model offers broad applicability for modeling turbulent combustion because of its good ability in representing the interaction between turbulence and chemical reaction. However, the highdimensional PDF transport equation is difficult to solve. Current methods to solve it include stochatisc Lagrangian Monte Carlo particle methods, Eulerian stochastic field methods, and quadrature-based methods of moments (QBMM). The last of which are deterministic and free from statistical fluctuation errors, and thus are attractive for calculating supersonic turbulent combustion [1]. In this work, we improve a QBMM named linear quadrature method of moments (LQMOM) [2]. Unlike the standard quadrature method of moments (QMOM) which uses Dirac delta functions to approximate the PDF, the LQMOM assumes the PDF is continuous and approximates the moments (integrals in the composition space) using a quadrature rule with N predefined quadrature nodes ψi and weights ωi. In this way, a linear system of equations is established for the unknown PDF values at the quadrature nodes, and the solution of which is cheaper than the product-difference/Wheeler algorithm in the QMOM. However, the LQMOM in [2] may solve negative PDF values when the exact PDF distribution is non-smooth, thus it has to be used with the parameter-tuning LQMOM-QMOM hybrid strategy. This flaw is remedied here by the following procedure. For the solved PDF values {f1, f2, . . . , fN}, we check whether the entry fi < 0 in the sequence of i = 1, . . . ,N. If fi ≥ 0 we proceed to the next i. Otherwise, we reset fi to zero by denoting the new value as Fi = 0, and scale down all the other entries using the formula Fk = fk · M0 NP j=1 ωj(ψj)0fj − ωi(ψi)0fi = fk · M0 NP j=1 ωjfj − ωifi , k = 1, . . . ,N, k ̸= i, (1) then assign the new value Fk to fk for k = 1, . . . ,N, and then proceed to the next i. This correction procedure ensures that all PDF values are non-negative and keeps the zero-order moment M0. The correction procedure is also applied to the Linear Conditional QMOM (LCQMOM) [2] for multivariate PDF cases. Finally, a temperature-consistency modification is made for the LES-PDF method, which is being tested in the 3D supersonic reacting air/H2 jet and the supersonic cavity stabilized combustor. In summary, the present modified LQMOM (LCQMOM) can be used independently, and is more efficient than the QMOM (CQMOM). The resulting LES-LCQMOM method is promising for modeling turbulent combustion, especially in supersonic regimes.