We propose in this article a Composite Logistic Regression (CLR) approach for ordinal panel data regression. The new method transforms the original ordinal regression problem into a number of binary ones. Thereafter, the method of conditional logistic regression (Chamberlain, 1984; Wooldridge, 2001; Hsiao, 2003) can be directly applied. As a result, the new method allows the unobserved subject effects to be correlated with the observed predictors in an arbitrary manner. Computationally, the new method is able to profile out unobserved subject effects in a very neat manner. This not only makes computational implementation very easy but also makes theoretical treatment straightforward. In particular, we show theoretically that the resulting estimator is n-consistent and asymptotically normal. Both simulations and a real example are reported to demonstrate the usefulness of the new method.