Drug-target interaction (DTI) prediction, which aims at predicting whether a drug will be bounded to a target, have received wide attention recently, with the goal to automate and accelerate the costly process of drug design. Most of the recently proposed methods use single drug-drug similarity and target-target similarity information for DTI prediction, which are unable to take advantage of the abundant information regarding various types of similarities between them. Very recently, some methods are proposed to leverage multi-similarity information, however, they still lack the ability to take into consideration the rich topological information of all sorts of knowledge bases where the drugs and targets reside in. More importantly, the time consumption of these approaches is very high, which prevents the usage of large-scale network information. We thus propose a network-based drug-target interaction prediction approach, which applies probabilistic soft logic (PSL) to meta-paths on a heterogeneous network that contains multiple sources of information, including drug-drug similarities, target-target similarities, drug-target interactions, and other potential information. Our approach is based on the PSL graphical model and uses meta-path counts instead of path instances to reduce the number of rule instances of PSL. We compare our model against five methods, on three open-source datasets. The experimental results show that our approach outperforms all the five baselines in terms of AUPR score and AUC score.