In this paper, a variable-precision approximate floating-point multiplier is proposed for energy efficient deep learning computation. The proposed architecture supports approximate multiplication with BFloat16 format. As the input and output activations of deep learning models usually follow normal distribution, inspired by the posit format, for numbers with different values, different precisions can be applied to represent them. In the proposed architecture, posit encoding is used to change the level of approximation, and the precision of the computation is controlled by the value of product exponent. For large exponent, smaller precision multiplication is applied to mantissa and for small exponent, higher precision computation is applied. Truncation is used as approximate method in the proposed design while the number of bit positions to be truncated is controlled by the values of the product exponent. The proposed design can achieve 19% area reduction and 42% power reduction compared to the normal BFloat16 multiplier. When applying the proposed multiplier in deep learning computation, almost the same accuracy as that of normal BFloat16 multiplier can be achieved.