We investigate the individual optimal consumption and investment problem of a risk averse agent with a stochastic labor income under relative liquidity constraints meaning the borrowing limit is stochastic and, in particular, is set to be a xed proportion of the current level of income over time. When the agent has a constant relative risk aversion utility function, we provide the explicit solution for the optimal consumption and investment policies. The optimal portfolio in our model does not approach to zero as the agent's wealth approaches to the borrowing limit and it can be positive and negative depending on the correlation between nancial risk and income risk. This result is the sharp contrast to that from the previous literature that considered the nonnegative wealth constraint. In addition, we show the optimal wealth process never hits the stochastic debt limit over time. We also illustrate numerical results of optimal policies.