Current status data arise due to only one feasible examination such that the failure time of interest occurs before or after the examination time. If the examination time is intrinsically related to the failure time of interest, the examination time is referred to as an informative censoring time. Such data may occur in many fields, for example, epidemiological surveys and animal carcinogenicity experiments. To avoid severely misleading inferences resulted from ignoring informative censoring, we propose a class of semiparametric transformation models with log-normal frailty for current status data with informative censoring. A shared frailty is used to account for the correlation between the failure time and censoring time. The expectation-maximization (EM) algorithm combining a sieve method for approximating an infinite-dimensional parameter is employed to estimate all parameters. To investigate finite sample properties of the proposed method, simulation studies are conducted, and a data set from a rodent tumorigenicity experiment is analyzed for illustrative purposes.