There has been a growing interest in language and literacy skills transfer; specifically, the amount, the conditions, and the contexts of such a transfer are under question in the transfer of the native language reading skills and those of the target language. In this descriptive study, we aim at investigating whether there is a relationship between the L1 and L2 cognitive academic language proficiency (CALP) of the graduate students whose medium of instruction is English. For this reason, we adapted the questionnaire prepared by Hellekjaer (2009) for Norwegian students. The participants were asked to self-assess themselves quantitatively. Firstly, the findings have indicated that the good reader in L1 is also a good reader in L2. So there is a positive transfer from L1 CALP into L2 CALP. The second finding is that reading texts in their field eases the comprehension of the texts since they use the context knowledge. The participants also seem to be transferring their L1 reading habits into L2 reading. For the poor readers, the lack of reading practices in their previous education life may be the reason for not being able to develop reading strategies. The results may shed light to enhance the reading skills of the English language learners, especially for academic purposes.