The reliability of deep neural networks (DNN) against hardware errors is essential as DNNs are increasingly employed in safety-critical applications such as automatic driving. Transient errors in memory, such as radiation-induced soft error, may propagate through the inference computation, resulting in unexpected output, which can adversely trigger catastrophic system failures. As a first step to tackle this problem, this paper proposes constructing a vulnerability model (VM) with a small number of fault injections to identify vulnerable model parameters in DNN. We reduce the number of bit locations for fault injection significantly and develop a flow to incrementally collect the training data, i.e., the fault injection results, for VM accuracy improvement. We enumerate key features (KF) that characterize the vulnerability of the parameters and use KF and the collected training data to construct VM. Experimental results show that VM can estimate vulnerabilities of all DNN model parameters only with 1/3490 computations compared with traditional fault injection-based vulnerability estimation.