This paper investigates the flow behavior of a viscous, incompressible and electrically conducting fluid in a long channel subjected to a time-varied oblique magnetic field B-0(t) = B(0)f(t). The time-dependent MHD equations are solved by using the dual reciprocity boundary element method (DRBEM). The transient level velocity and induced magnetic field profiles are presented for moderate Hartmann number values, several direction of applied magnetic field and for several functions f(t) as polynomial, exponential, trigonometric, impulse and step functions. It is observed that, when f(t) is a polynomial or exponential function, the velocity magnitude increases up to a certain time level where the flow shows an elliptical elongation and then starts to decrease for all values of Hartmann numbers. For the trigonometric function f(t), the flow repeats its behavior with a period. An impulse function changes flow behavior with an elongation at the level where the impulse is applied to the magnetic field. Then, it behaves as if a uniform magnetic field is applied. Having a step function f(t), the behavior of the flow shows both impulse and polynomial functions features. This study shows that time-varied magnetic field changes the flow behavior significantly at all the transient levels.