This articles deals with unsteady MHD free convection flow of blood with carbon nanotubes. The flow is over an oscillating vertical plate embedded in a porous medium. Both single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs) are used with human blood as base fluid. The problem is modelled and then solved for exact solution using the Laplace transform technique. Expressions for velocity and temperature are determined and expressed in terms of complementary error functions. Results are plotted and discussed for embedded parameters. It is observed that velocity decreases with increasing CNTs volume fraction and an increase in CNTs volume fraction increases the blood temperature, which leads to an increase in the heat transfer rates. A validation of the present work is shown by comparing the current results with existing literature.