An interpolation computational ghost imaging (ICGI) method is proposed and demonstrated that is able to reduce the noise interference from a fluctuating source and background. The noise is estimated through periodic illuminations by a specific assay pattern during sampling, which is then used to correct the bucket detector signal. To validate this method simulations and experiments were conducted. Light source intensity and background lighting were randomly varied to modulate the noise. The results show that good quality images can be obtained, while with conventional computational ghost imaging (CGI) the reconstructed object is barely recognizable. The ICGI method offers a general approach applicable to all CGI techniques, which can attenuate the interference from source fluctuations, background light noise, dynamic scattering, and so on.