Machine Learning as a Service (MLaaS) allows clients with limited resources to outsource their expensive ML tasks to powerful servers. Despite the huge benefits, current MLaaS solutions still lack strong assurances on: 1) service correctness (i.e., whether the MLaaS works as expected); 2) trustworthy accounting (i.e., whether the bill for the MLaaS resource consumption is correctly accounted); 3) fair payment (i.e., whether a client gets the entire MLaaS result before making the payment). Without these assurances, unfaithful service providers can return improperly-executed ML task results or partially trained ML models while asking for over-claimed rewards. Moreover, it is hard to argue for wide adoption of MLaaS to both the client and the service provider, especially in the open market without a trusted third party. In this paper, we present VeriML, a novel and efficient framework to bring integrity assurances and fair payments to MLaaS. With VeriML, clients can be assured that ML tasks are correctly executed on an untrusted server and the resource consumption claimed by the service provider equals to the actual workload. We strategically use succinct non-interactive arguments of knowledge (SNARK) on randomly-selected iterations during the ML training phase for efficiency with tunable probabilistic assurance. We also develop multiple ML-specific optimizations to the arithmetic circuit required by SNARK. Our system implements six common algorithms: linear regression, logistic regression, neural network, support vector machine, Kmeans and decision tree. The experimental results have validated the practical performance of VeriML.