Because the sizes of samples differ in x-ray micro-CT applications, it is desirable to have a mechanism to change the field of view of a micro-CT scanner. A well-known way to double the diameter of the field of view is to displace a detector array by 50%. In this paper, we propose to displace a detector array by an amount of greater than 0% but less than 50% for a continuously adjustable field of view, and formulate a weighting scheme for artifact-free reconstruction. Then, we perform numerical simulation with the Shepp-Logan phantom to demonstrate the feasibility in fan-beam and cone-beam geometry.