The increasing attention on Bitcoin since 2013 prompts the issue of possible evidence for a causal relationship between the Bitcoin market and internet attention. Taking the Google search volume index as the measure of internet attention, time-varying Granger causality between the global Bitcoin market and internet attention is examined. Empirical results show a strong Granger causal relationship between internet attention and trading volume. Moreover, they indicate, beginning in early 2018, an even stronger impact of trading volume on internet attention, which is consistent with the rapid increase in Bitcoin users following the 2017 Bitcoin bubble. Although Bitcoin returns are found to strongly affect internet attention, internet attention only occasionally affects Bitcoin returns. Further investigation reveals that interactions between internet attention and returns can be amplified by extreme changes in prices, and internet attention is more likely to lead to returns during Bitcoin bubbles. These empirical findings shed light on cryptocurrency investor attention theory and imply trading strategy in Bitcoin markets.