rental cost of capital I am estimating time series for rental price of capital using Hall-Jorgenson method: $$r=\frac{P_k}{P}(i-inf+\delta)$$
here, $r$ is the rental cost of capital, $P_k$ is the price of capital goods (price index for capital goods), $P$ is a deflator, $i$ is nominal interest rate, $inf$ is an inflation rate and $\delta$ is depreciation rate of physical capital stock.

Because inflation rate is high in some periods, the rental cost of capital is negative for these periods; this does not make sense, any little help is welcome!
In theory there is nothing that is preventing the real interest rate from becoming negative. Making the real interest rate negative by keeping the nominal rate at zero and creating inflation has been the goal of the ECB in the recent past. Once you hit the ZLB there is no other way to further loosen monetary policy. With regard to your work it is probably important to carefully select the inflation rate you're using, but you dont describe this in detail. Depending on your question you might want to consider forward looking measures (i.e.Blue Chip or Greenbook forecasts if you're talking about the US).