Current methods for the assessment of amphibian population abundance and density are either invasive and time-consuming, or qualitative and subject to unquantifiable observer biases. 2. We propose an acoustic spatially explicit capture-recapture (SECR) method to estimate population abundance and density for calling frog species, which avoids the problems above. It produces an estimate of call density which can be converted to frog density by using call rate data. Time-of-arrival and signal strength data are used to achieve better accuracy than is possible using a standard SECR approach. Lack of independence of detections is a problem when individuals can't be identified from their call, and we suggest a bootstrap-like approach to calculate standard errors and interval estimates. 3. We estimate frog density and associated uncertainty from an acoustic survey of the Cape Peninsula moss frog Arthroleptella lightfooti. Through simulation studies, we show that our method leads to unbiased density estimates and standard errors. 4. This acoustic SECR approach is cheaper, faster, and more statistically rigorous than other approaches of monitoring calling anuran populations. Our method has wider applications, and can be used for many species that can be detected on a microphone array.