Eulerian methods are popular for describing particle dispersion and reaction in gas-particle two-phase flow simulations. However, for problems with wide Particle Size Distributions (PSD), such as those associated with coal combustion, the PSD has to be represented by a limited number of particle sizes in order to decrease the computational costs of the transport equations. The objective of this study is to investigate the effects of the number of particle sizes on the Eulerian LES simulation of a pulverized coal jet flame. In this study, experimental work on a Hencken-type entrained flow reactor was carried out to provide the validation data of flame ignition distances. A simplified Direct Quadrature Method of Moments (DQMOM) method was proposed in order to decrease the computation cost in the Eulerian framework. Several simulation cases with different quadrature nodes (particle sizes) were conducted. The flame ignition distance was well predicted when two and more quadrature nodes were adopted in the simulation. But it was overestimated when only one quadrature node was considered. So one particle size is not enough to represent a wide PSD of coal in the Eulerian LES simulation of pulverized coal flames. When 5 particle sizes were adopted in the simulation, the ignition distances and time-variant fluctuations can be well predicted when compared with experimental results under different operating conditions. This study shows that LES with the simplified DQMOM method can describe the ignition distance in gas-solid two-phase reacting flows even with only a few quadrature nodes.