Effective thermal conductivity of a unary (mono-sized) pebble bed depends on the physical properties of solid pebbles, physical properties and flow rate of fluid, temperature, coordination number of pebbles, and void fraction. The pebble size also plays an important role on the effective thermal conductivity of a unary pebble bed. To date, no theoretical justification for the same has been reported. In this present study an attempt was made to justify theoretically the dependence of the effective thermal conductivity on pebble size of a unary pebble bed filled with a stagnant fluid. A mathematical model has been developed to determine the effective thermal conductivity of a unary pebble bed with stagnant fluid. Different particle sizes (10m to 10mm) were considered and modes of heat transfer were assumed to be conduction and convention only. Radiation mode of heat transfer was not considered. It was found that the effective thermal conductivity depends on the pebble size and the estimated values of the same were in close agreement with the reported experimental results.