OTC markets exhibit a core-periphery interdealer network: 10-30 central dealers trade frequently and with many dealers, while hundreds of peripheral dealers trade sparsely and with few dealers. Existing work rationalize this phenomenon with exogenous dealer heterogeneity. We build a directed search model of network formation and propose that a core-periphery network arises from specialization. Dealers endogenously specialize in different clients with different liquidity needs. The clientele difference across dealers, in turn, generates dealer heterogeneity and the core-periphery network: The dealers specializing in clients who trade frequently form the core, while the dealers specializing in buy-and-hold investors form the periphery.