Nowadays voice search for points of interest (POI) is becoming increasingly popular. However, speech recognition for local POI has remained to be a challenge due to multi-dialect and massive POI. This paper improves speech recognition accuracy for local POI from two aspects. Firstly, a geographic acoustic model (Geo-AM) is proposed. The Geo-AM deals with multi-dialect problem using dialect-specific input feature and dialect-specific top layer. Secondly, a group of geo-specific language models (Geo-LMs) are integrated into our speech recognition system to improve recognition accuracy of long tail and homophone POI. During decoding, specific language models are selected on demand according to users' geographic location. Experiments show that the proposed Geo-AM achieves 6.5%$\sim$10.1% relative character error rate (CER) reduction on an accent testset and the proposed Geo-AM and Geo-LM totally achieve over 18.7% relative CER reduction on Tencent Map task.