fNIRS (functional near-Infrared spectroscopy) can measure brain activity non-invasively and has advantages such as low cost and portability. While the conventional fNIRS has used laser light, LED light fNIRS is recently becoming common in use. Using LED for fNIRS, equipment can be more inexpensive and more portable. LED light, however, has a wider illumination spectrum than laser light, which may change crosstalk between the calculated concentration change of oxygenated and deoxygenated hemoglobins. The crosstalk is caused by difference in light path length in the head tissues depending on wavelengths used. We conducted Monte Carlo simulations of photon propagation in the tissue layers of head (scalp, skull, CSF, gray matter, and white matter) to estimate the light path length in each layers. Based on the estimated path lengths, the crosstalk in fNIRS using LED light was calculated. Our results showed that LED light more increases the crosstalk than laser light does when certain combinations of wavelengths were adopted. Even in such cases, the crosstalk increased by using LED light can be effectively suppressed by replacing the value of extinction coefficients used in the hemoglobin calculation to their weighted average over illumination spectrum.